Below we provide a list of indispensable bibliography, some advice on how to navigate life as a scientist, as well as work data made freely available to the community from the CoG. If you can’t find the material you are looking for or if something is unclear, please contact us.
Gravity and General Relativity
R. Arnowitt, S. Deser, C. W. Misner. The Dynamics of General Relativity
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This article summarizes the authors’ novel formulation of General Relativity, which played and continues to play a fundamental role in numerical relativity, approaches to quantum gravity, etc.
J. D. Bekenstein. Black Holes and Entropy.
One of the greats. Bekenstein introduces the concept of entropy based solely on analogy between the laws of black hole mechanics and thermodynamics.
J. D. Bekenstein. Generalized Second Law of Thermodynamics in Black-Hole Physics
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…and now Bekenstein shows the generalized second law of black hole mechanics, together with a few other consequences.
D. R. Brill and J. A. Wheeler. Interaction of Neutrinos and Gravitational Fields.
Gravitational effects on the physics of neutrinos. Still a classic. It includes the identification of spin-orbit coupling terms, comparisons of energy spectrum with other particles, neutrino pair creation without beta interactions, etc, and finally the constitution of a geon.
C. Will. The Confrontation between General Relativity and Experiment
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How well does General Relativity describe the gravitational interaction? The answer is here. From the post-Newtonian framework to all sorts of magnificent tests.
M. Colpi, S. L. Shapiro and I. Wasserman.
Boson Stars Gravitational Equilibria of Self Interacting Scalar Fields.
Generalizes Ruffini and Bonazzola’s construction to self-interacting fields. The literature is huge. See the review by Liebling and Palenzuela.
T. Damour and G. Esposito-Farèse. Nonperturbative Strong Field Effects in Tensor Scalar Theories of Gravitation
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First introduction to the concept of spontaneous scalarization: non trivial scalar profiles stars in scalar-tensor theories, triggered by high compactness (avoiding solar system constraints). The authors show how it gives rise to interesting new channels of radiation.
T. Damour and G. Esposito-Farèse. Tensor Scalar Gravity and Binary Pulsar Experiments
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Thorough investigation of non perturbative effects (i.e. spontaneous scalarization) around static and slowly rotating neutron stars. The analogy with spontaneous ferromagnetism is developed, as well as the confrontation with binary pulsar observations.
J. B. Hartle. Slowly Rotating Relativistic Stars, Part I
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A complete relativistic extension of the Newtonian theory is presented here. Hartle derives the equations describing a relativistic star in hydrostatic equilibrium using a second order approximation in the angular velocity.
J. B. Hartle and K. S. Thorne. Slowly Rotating Relativistic Stars, Part II
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In this second work, equations derived in Paper I are solved numerically for different equations of state. In particular, the authors focus on white dwarfs, neutron stars and supermassive stars.
S. Hawking. Gravitationally Collapsed Objects of Very Low Mass
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Hawking develops the physics of primordial black holes. Very light black holes should evaporate in a flash and not survive till today. More massive black holes can. Primordial black holes as source of recent GW observations are in fashion. For recent reviews see Carr.
V. Kalogera and G. Baym. The Maximum Mass of a Neutron Star.
Neutron stars should not have more than 2.9 solar masses. The absolute maximum mass of a neutron star provides a decisive method of observationally distinguishing neutron stars from black holes.
L. Lehner, R. C. Myers, E. Poisson and R. D. Sorkin
. Gravitational Action With Null Boundaries.
A self-contained and detailed source on the action functional of general relativity, discussing boundaries of all types (spacelike, timelike, null). Known results are collected and the ambiguities of null boundaries are clarified. A useful "Action user's manual" is provided at the end.
R. Maartens and B. A Bassett.
Gravito Electromagnetism.
An almost perfect analogy between electromagnetism and gravity was laid down by Heaviside in 1893. The authors show how it carries, in a rigorous way, to General Relativity.
J. R. Oppenheimer and H. Snyder. On continued Gravitational Contraction
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The first study of gravitational collapse to the very end of it. This classic taught us how collapse proceeds and how we should think about black holes.
C. E. Rhoades and R. Ruffini. Maximum Mass of a Neutron Star.
On the basis of Einstein's theory of relativity, the principle of causality, and Le Chatelier's principle, it is here established that the maximum mass of the equilibrium configuration of a neutron star cannot be larger than 3.2 solar masses. You need to read also Oppenheimer and Volkoff.
R. Penrose. Gravitational collapse and spacetime singularities.
Physically reasonable spacetimes are singular. This realization was extended in different ways, see also Natário’s exposition.
R. Penrose. Gravitational Collapse: The Role of General Relativity
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Gravitational collapse leads to singularities, so Penrose decised a cosmic censor! He also understood how to extract energy from rotating black holes, using test particles and the existence of ergoregions in curved spacetimes (important generalizations by Piran and Schnittman).
R. Ruffini and S. Bonazzola. Systems-of-Self Gravitating Particles in General Relativity and the Concept of an Equation of State.
Expanding on Wheeler’s geons, this work deals with the physics and mathematics of self-gravitating bound systems formed by fermions or bosons. Boson stars descend from this classic.
R. M. Wald. Black Hole Entropy is Noether Charge.
The first law of black hole mechanics is not special to General Relativity!
J. A. Wheeler. Geons
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Can waves be trapped by their own gravity, forming gravitational entities, geons? Can we explain elementary particles or electromagnetism without singularities in this way? This is what this seminal work deals with.
E. Witten. Light Rays Singularities and All That
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An introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem
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Zel'dovitch and Novikov. The Hypothesis of Cores Retarded During Expansion and the Hot Cosmological Model
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Zel'dovitch & Novikov deal with primordial black holes in 1966.
Black Holes
A. Arvanitaki and S. Dubovsky. Exploring the String Axiverse with Precision Black Hole Physics
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Superradiant instabilities attracted attention because their turn anti-de Sitter spacetimes unstable, and because they can be used to constraint the matter content of the universe. This paper started it. See also the Lecture Notes by Brito et al.
J. M. Bardeen, W. H. Press, S. A. Teukolsky. Rotating Black-Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation.
Everyting you wanted to know about the Kerr spacetime is here.
D. Baumann, H. S. Chia and R. A. Porto. Probing ultralight bosons with binary black holes
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This is an elegant analysis of superradiant clouds and tidal effects using tools borrowed from quantum mechanics.
T. Binnington and E. Poisson. Relativistic theory of tidal Love numbers
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Develops the formalism to study stationary tidal deformations in GR and applies it to compute the tidal Love numbers of neutron stars (see also chapter 2.5 of Poisson and Will and Hinderer and Flanagan’s seminal work).
V. Cardoso, J. L. Costa, K. Destounis, P. Hintz and A. Jansen. Quasinormal Modes and Strong Cosmic Censorship
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Classical, Strong Cosmic Censorship may not be upheld in de Sitter spacetimes, in the presence of charge. See also Hollands et al, for possible impact of quantum effects.
V. Cardoso, Ó. J. C. Dias, J. P. S. Lemos and S. Yoshida. The Black Hole Bomb and Superradiant Instabilities
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This is one example of Press and Teukolsky’s predictions, shown to be correct: the black-hole bomb. This work also predicted the instability of rotating black holes in anti-de Sitter Universe, shown later to be correct, see Cardoso et al.
V. Cardoso, E. Franzin and P. Pani. Is the Gravitational-Wave Ringdown a Probe of the Event Horizon?
No. Ringdown, as seen by LIGO, is related to the photon sphere. In the absence of horizons, echoes of the original signal will dictate the late time relaxation. See review by Cardoso and Pani.
V. Cardoso and P. Pani. Testing the Nature of Dark Compact Objects: a Status Report
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Do black holes exist? How can we quantify the presence of horizons in our universe?
S. Chandrasekhar and V. Ferrari. On the non-radial Oscillations of a star III.
A reconsideration of the Axial Modes
A classic, and not only on black hole physics.
M. W. Choptuik. Universality and Scaling in Gravitational Collapse of a Massless Scalar Field
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Minkowski is stable, but large initial data collapses to black holes. What happens at the threshold of black hole formation? Choptuik’s remarkable study finds critical phenomena, power-law scaling and echoing. The ‘critical solution between collapse and dispersion is an example of a naked singularity. See Gundlach & Martı́n-Garcı́a's overview.
N. Comins and B. F. Schutz. On the Ergoregion Instability
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Spacetimes with ergoregions but without horizons are unstable. See follow-up by Moschidis, and physical consequences in the Lecture Notes by Brito et al.
E. Curiel. The Many Definitions of a Black Hole.
Decades after the understanding of black hole spacetimes, black holes are still cause for debate. Here’s an excellent discussion on what black holes are, from various viewpoints.
T. Damour and A. Nagar. Relativistic Tidal Properties of Neutron Stars.
Very similar work to “Relativistic theory of tidal Love numbers” by Binnington and Poisson (written independently by the two groups and published at the same time).
S. Chandrasekhar and S. Detweiler. The Quasi-Normal Modes of the Schwarzschild Black Hole
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Chandrasekhar and Detweiler’s classic, where a direct integration method is used to compute, for the first time, the quasinormal modes of black holes.
S. Detweiler. Klein-Gordon Equation and Rotating Black Holes.
A small fluctuation of a light scalar field will grow exponentially close to a rotating black hole. This was shown via matched asymptotics, and establishes the proposal by Damour, Deruelle & Ruffini and the WKB results by Zouros and Eardley.
S. R. Dolan. Instability of the Massive Klein-Gordon Field on the Kerr Spacetime
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The results by Detweiler were confirmed numerically by Cardoso & Yoshida (and shown not to extend to higher dimensions). Later, Sam Dolan explored thoroughly the subject in this beautiful work.
V. Ferrari and B. Mashhoon. New Approach to the Quasi-Normal Modes of a Black Hole.
A relation is established between the null circular geodesics and the quasinormal modes. The derivation was simplified and the results extended to arbitrary spacetimes in Cardoso et al (2009).
É. É. Flanagan and T. Hinderer. Constraining Neutron-Star Tidal Love Numbers with Gravitational-Wave Detectors
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Here’s how to use LIGO observations to measure the tidal Love numbers of neutron stars (which have by now been measured), but the formalism can be extended to any GW detector and compact object.
S. E. Gralla and T. Jacobson. Spacetime Approach to Force-Free Magnetospheres.
An elegant description of force-free environments, opening a new window into this subjectType a message.
S. W. Hawking. Particle Creation by Black Holes
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Yes, black holes evaporate once quantum mechanics is brought into the game. This work was refined in many different ways, including the calculation of greybody factors by Don Page, and many many other issues.
C. Herdeiro and E. Radu. Kerr Black Holes with Scalar Hair
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Theorems are valid under certain assumptions…when these are not met, new things happen. A black hole surrounded by a scalar field is possible as an equilibrium solution of the field equations.
R. Kerr. Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics.
The 1963 work where the Kerr geometry is shown for the first time.
E. W. Leaver. An Analytic Representation for the Quasi-Normal Modes of Kerr Black Holes.
…and Leaver’s continued fraction representation, which is the state of the art in what regards precision of QNM frequency calculation. See review 1, review 2 and review 3 as well.
S. Mano, H. Suzuki and E. Takasugi. Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions
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The title says it all, an important reference in black hole physics, allowing accurate calculations of waveforms.
J. Michell. On the Means of Discovering the Distance, Magnitude…
We think of black holes as a 20th century invention, dating back to 1916. But the true “father” of the black hole concept was a humble 18th century English rector named John Michell–a man so far ahead of his scientific contemporaries that his ideas languished in obscurity.
V. Moncrief. Stability of Stationary, Spherical Accretion onto a Schwarzschild Black Hole
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This work is remarkable because it predates Unruh’s: Moncrief shows, studying relativistic hydrodynamics of accretion flows surrounding black holes, that an effective metric arises. Sound waves “see” a metric that is controlled by the background flow.
Y. Mino, M. Sasaki, M. Shibata, H. Tagoshi and T. Tanaka. Black Hole Perturbation.
A compendium on analytical and numerical results for collapse and gravitational radiation by point particles around black holes.
E. Poisson, C. Cutler, L. S. Finn, G. J. Sussman. Gravitational Radiation from a Particle in Circular Orbit Around a Black-Hole II.
Analytical Results for the Nonrotating Case
Continuation of the above work, it had to be on this list too. See also follow ups, papers III, IV, etc.
E. Poisson and W. Israel. Inner-Horizon Instability and Mass Inlation in Black Holes.
Some black hole spacetimes have Cauchy horizons, signalling the breakdown of physics (of predictability). Fortunately Poisson and Israel showed that they are unstable, uncovering a (Strong) Cosmic Censor.
W. H. Press. Long Wave Trains of Gravitational Waves from a Vibrating Black Hole.
Here’s how Press estimates analytically the quasinormal mode frequencies.
T. Regge and J. A. Wheeler. Stability of a Schwarzschild Singularity.
This classic, done before black holes were even accepted, teaches us how to separate gravitational fluctuations with tensor harmonics.
R. Price. Nonspherical Perturbations of Relativistic Gravitational Collapse. I. Scalar and Gravitational Perturbations.
After ringdown, backscattering off spacetime curvature gives rise to power-law tails. These are Price’s tails, completing the approach to a no-hair object…but tails are generic features of curved spacetime.
D. C. Robinson. Uniqueness of the Kerr Black Hole.
And, extending the work by Israel, Robinson shows that Kerr is unique! This is part of the uniqueness or no-hair results in black hole physics. For more recent reviews, see Chrusciel & Costa, Cardoso & Gualtieri, Herdeiro & Radu, and Israel’s account in 300 Years of Gravitation.
B. F. Schutz and C. M. Will. Black Hole Normal Modes: A Semianalytic Approach
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A WKB approach to the quasinormal modes of black holes. See improvements by Konoplya and Matyjasek & Telecka.
R. F. Stark and T. Piran. Gravitational-Wave Emission from Rotating Gravitational Collapse
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Pioneering work on gravitational wave emission from collapse with angular momentum.
W. Press and S. Teukolsky. Floating Orbits, Superradiant Scattering, and the Black-Hole Bomb.
A delight to read. Superradiance is claimed to give rise to instabilities and strange orbital phenomena. All of these predictions were later confirmed. See the Lecture Notes by Brito et al for a comprehensive overview.
S. A. Teukolsky. Perturbations of a Rotating Black Hole I.
Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations
Regge-Wheeler-Zerilli’s approach doesn’t work with rotation. But Teukolsky showed how to study, decouple and separate linearized fluctuations in a Newman-Penrose approach. See also the follow-ups by Teukolsky and Press.
W. Unruh. Notes on Black-Hole evaporation
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Unruh looks into a number of aspects related to Hawking radiation. Among others, he shows that accelerated detectors must also see radiation, even in flat spacetime.
W. Unruh. Experimental Black-Hole evaporation
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Unruh realizes, independently from Moncrief, that fluid dynamics can mimic some aspects of general relativity. In particular, sound waves behave formally as a scalar field in curved spacetime. Water can mimic black holes! Analogue gravity now has a long history, see the reviews by Visser and Barceló et al.
C. V. Vishveshwara. Scattering of Gravitational Radiation by a Schwarzschild Black Hole
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Black holes have no hair…but how do they lose it? Here’s a classic: the scattering of Gaussian pulses show that fluctuations die off as damped sinusoids. These are the characteristic vibration modes of black holes, the quasinormal modes. See review 1, review 2, and review 3 for the state of the art.
Y. Zel’dovich. Amplification of Cylindrical Electromagnetic Waves Reflected from Rotating Body
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Zel’dovich shows that rotating bodies are able to amplify low-frequency radiation. This classical process is known as superradiance, the analogue of the Penrose process for waves. For a recent review on this process see these Lecture Notes from Springer.
F. J. Zerilli. Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics
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Continuing Regge and Wheeler’s work, Zerilli combined the polar gravitational fluctuations into a single master function. It’s a classic with a number of typos (see Berti’s list of typos)
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Gravitational Waves
A. Buonanno and T. Damour. Transition from Inspiral to Plunge in Binary Black Hole Coalescences
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A remarkable work in which the nascent EOB formalism was used to provide, for the first time, a complete model for the gravitational waveform for the inspiral, merger and ringdown of a binary black hole system.
T. A. Apostolatos, C. Cutler, G. Sussman and K. S. Thorne. Spin-Induced Orbital Precession and its Modulation of the Gravitational from Merging Binaries
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When at least one constituent of a compact binary system is (generically) spinning the orbital plane will precess. The resulting modulation of the waveform is both subtle and interesting. Here the authors use a PN approach to describe this behavior.
E. Berti, A. Buonanno and C. M. Will. Estimating Spinning Binary Parameters and Testing Alternative Theories of Gravity with LISA
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The determination of binary parameters from waveforms is crucial. The authors examine binaries relevant to space-based detectors, within both GR and alternative theories. They find orders of magnitude degradation in the determination for alternative theories.
E. Berti, V. Cardoso and C. M. Will. Gravitational-Wave Spectroscopy of Massive Black Holes with the Space Interferometer LISA
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Presentation of a formalism to detect ringdown signals, from which parameters of the associated BHs can be read off. The associated SNR for LISA is examined.
E. Berti, V. Cardoso J. A. Gonzalez, U. Sperhake, M. Hannam, S. Husa and B. Brügmann. Inspiral, Merger, and Ringdown of Unequal Mass Black Hole Binaries: A Multipolar Analysis.
BBHs of different mass ratios are studied. Numerical data are compared to PN results and the relative strengths of the multipoles examined. Again the PN results are surprisingly good (at least in comparison with the expectations of the time).
A. Buonanno, G. B. Cook and F. Pretorius. Inspiral, Merger, and Ring-Down of Equal-Mass Black-Hole Binaries.
Here, in one of the first works towards the systematic interface of numerical and analytical relativity, BBHs of equal mass ratio are studied. The PN approximation gradually becomes less accurate through the inspiral, but specific quantities are surprisingly well-described.
A. Buonanno and T. Damour. Effective One-Body Approach to General Relativistic Two-Body Dynamics.
In a fantastic, and fantastically influential paper, an approach for modeling the relativistic two-body problem is introduced. The idea is to map the dynamics on to that of a test body moving in an effective spacetime. EOB is now used in most GW data analysis.
A. Buonanno, B. R. Iyer, E. Ochsner, Y. Pan, and B. S. Sathyaprakash. Comparison of Post-Newtonian Templates for Compact Binary Inspiral Signals in Gravitational-Wave Detectors
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There are various PN approximations even at the same (formal) expansion order. In this paper different approximations are compared with each other and with EOB. For small binaries all behave comparably for detection. For large mass binaries EOB is favorable.
C. Cutler, D. Kennefick and E. Poisson. Gravitational Radiation Reaction for Bound Motion Around a Schwarzschild Black Hole
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An elegant description of gravitational wave generation by “point particles” (stars or stellar-mass BHs) around large black holes. Analytical results are worked out, and the procedure to expand in higher powers of velocity is laid out. Beautiful.
C. Cutler and E. E. Flanagan. Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral waveform?
An important study of the extraction of binary parameters from the waveform. Particular attention is paid to the obstruction that spin plays to the evaluation of the constituent masses.
C. Cutler. Angular Resolution of the LISA Gravitational Wave Detector
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The strategy for source characterization for a (single) space based detector necessarily differs from that of a network of ground-based detectors. In this paper the determination of source position is considered for such an experiment.
C. Cutler, T. A. Apostolatos, L. Bildsten, L. S. Finn, E. E. Flanagan, D. Kennefick, D. M. Markovic, A. Ori, E. Poisson, G. J. Sussman and K. S. Thorne. The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
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Everything you want to know about neutron stars and gravitational wave detection is somehow condensed here, at a time when neutron stars were thought to be the most abundant sources of gravitational waves.
S. Detweiler. Pulsar Timing Measurements and the Search for Gravitational Waves
A true classic.
Detweiler understand how to use an array of pulsars as clocks, with which to detect the passing of a gravitational wave.
S. Droz, D. J. Knapp, E. Poisson and B. J. Owen. Gravitational Waves from Inspiraling Compact Binaries: Validity of the Stationary-Phase Approximation to the Fourier Transform
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The title says it all.
L. S. Finn and D. F. Chernoff. Observing Binary Inspiral in Gravitational Radiation One Interferometer
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All of the enchilada of physics and data analysis necessary to claim a detection of gravitational waves is explored here. See also Flanagan and Hughes' classic.
L. S. Finn. Detection Measurement and Gravitational Radiation.
If you want to know how gravitational waves are detected, start by reading this.
É. É. Flanagan and S. A. Hughes. Measuring Gravitational Waves from Binary Black Hole Coalescences. I.
Signal to Noise for Inspiral, Merger, and Ringdown
. Just read it.
E. Poisson. Gravitational Radiation from a Particle in Circular Orbit Around a Black-Hole I. Analytical Results for the Nonrotating Case
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An elegant description of gravitational wave generation by “point particles” (stars or stellar-mass BHs) around large black holes. Analytical results are worked out, and the procedure to expand in higher powers of velocity is laid out. Beautiful.
F. Pretorius. Evolution of Binary Black-Hole Spacetimes.
Pretorius presents for the first time a solution to the two-body problem in general relativity: a non-linear evolution of a black hole binary through inspiral, merger, and ringdown. The numerical code employed uses generalized harmonic coordinates to evolve the system and the gravitational wave signal emitted during merger. This was an outstanding problem in gravity and marks a major breakthrough in the field of numerical relativity.
K. S. Thorne and J. B. Hartle. Laws of Motion and precession for Black Holes and Other Bodies.
Corrections to the geodesic law of motion and Fermi-Walker law of transport, due to the coupling of a body's angular momentum and quadrupole moment to the Riemann curvature of the surrounding spacetime, are derived for any isolated body with slowly varying multipole moments.
K. S. Thorne. Gravitational-Wave Bursts with Memory: The Christodoulou Effect
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The memory of a GW burst is a permanent relative displacement between free test masses. The Christodoulou memory arises from nonlinearities in the Einstein equations. This article estimates its order of magnitude as well as its detection prospects for ground-based and space interferometers.
K. S. Thorne. Multipole Expansions of Gravitational Radiation
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A consolidation of the different multipole expansion formalisms developed in the literature of gravitation. In addition, Thorne introduces the "local wave zone" and provides algorithms and formulas for analytic approximations of gravitational radiation, widely used thereafter.
A. G. Wiseman and C. M. Will. Christodoulous Nonlinear Gravitational Wave Memory Evaluation in the Quadrupole Approximation
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The nonlinear memory effect is caused by the stress-energy of a gravitational wave itself and induces a 10% correction to the leading waveform for BNS systems.
Astrophysics
E. Berti and M. Volonteri. Cosmological Black Hole Spin Evolution by Mergers and Accretion
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How large is the spin of black holes in the cosmos?
R. D. Blandford and R. L. Znajek. Electromagnetic Extraction of Energy from Kerr Black Holes
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Although still unclear in some aspects, here’s a way that black holes can power luminous events.
S. Chandrasekhar. Dynamical Friction.
Dynamical friction on stars in the universe, caused by gravitational drag. A true classic.
F. Hoyle and R. A. Lyttleton. On The Accretion Theory of Stellar Evolution.
Initiates the study of accretion onto compact objects. See the follow ups by Bondi & Hoyle and Bondi and a more recent review.
E. Ostriker. Dynamical Friction in a Gaseous Medium
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Chandrasekhar’s theory applies to collisionless media. Here’s an elegant and classical work on the gaseous counterpart. Generalizations to slab-like geometries was done by Vicente et al, and the calculation of dynamical friction when the medium is a scalar field was done by Annulli et al.
H. Bondi and F. Hoyle. On the Mechanism of Accretion by Stars
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The classic on spherically symmetric steady accretion of matter by a black hole. For a recent review see. For similar processes with fundamental fields, of arbitrary Compton wavelength, see the work by Unruh.
N. I. Shakura and R. A. Sunyaev. Black Holes in binary Systems. Observational Appearance
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A classic on accretion disks.
I. D. Novikov and K. S. Thorne. Astrophysics of Black Holes
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Everything you need to know to understand accretion disk around black holes. You should read the classic by Shakura-Sunyaev and this more recent Living Reviews on accretion disks by Abramowicz and Fragile.
K. S. Thorne. Disk Accretion onto a Black Hole II.
Evolution of the Hole
Heating effects, together with absorption cross section which is larger for counter-rotating photons, imposes a maximum limit on the black hole spin, J=0.998 M^2.
M. C. Begelman, M. Volonteri and M. J. Rees. Formation of Supermassive Black Holes by Direct Collapse in Pre-Galactic Haloes
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A formation mechanism of black holes: the “direct collapse” model for black hole seeds.
J. Bardeen. Kerr Metric Black Holes
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The work that convinced the community to stop using Schwarzschild as a description of black holes. Accretion spins black holes up effectively.
“The pursuit of science has often been compared to the scaling of mountains, high and not so high. But who amongst us can hope, even in imagination, to scale the Everest and reach its summit when the sky is blue and the air is still, and in the stillness of the air survey the entire Himalayan range in the dazzling white of the snow stretching to infinity? None of us can hope for a comparable vision of nature and of the universe around us. But there is nothing mean or lowly in standing in the valley below and awaiting the sun to rise over Kinchinjunga.”
Subrahmanyan Chandrasekhar, Truth and Beauty: Aesthetics and Motivations in Science (1987), 26.
Work Ethics
Work. Work. Work. Do a calculation a day to keep bad spirits away.
Be punctual. Nobody likes to wait. If you value other people’s time, they will return the kindness.
Read. Read a lot. A great part of a researcher’s job is spent reading. Below, you can find some tips on how to guide yourself through the avalanche of papers that comes out daily on arXiv or in specialized journals. As an active researcher, you simply must know what the community is working on and what breakthroughs are being made. Many good researchers start their day checking the arXiv, an open repository where the latest research is published on a daily basis. Check the arXiv daily and read (at least) a paper per day. You don’t need to understand every detail of the work in question. As you read, try to understand the problem that the authors are addressing, why the problem is interesting, and how the authors are solving the problem. Trying to get the gist of the argument is of essence. Even if this is not immediately clear to you at the time, it will provide you with important tools for your work. Knowing what to read is a learning process. The more papers you go through, the easier it becomes to sort the good from the bad. Be active during journal clubs. Finally, checking good pop science magazines can help you in catching important works you missed.
Discuss. There’s a lot of clever people around you. Pick their brains and force them to pick yours. Go beyond what everyone did.
Be an explorer. Don’t close yourself in your little bubble. There’s a whole wild world out there. If you’re a theoretician, learn numerical methods and data analysis. If you’re a data analyst, learn the theoretical basis of what you’re doing. Learn new tools, new methods, learn. You’ll soon be rewarded.
Presentations
Public speaking may be daunting, but if you want to pursue an academic or research career you will have to present your work to the community. This means that you need to know how to talk in front of an audience. The most common way to do this is through seminars. Your calculations will not be read nor understood until you convince others that they are important and relevant. Promoting your work is a key part in establishing yourself in the scientific community. A good talk or presentation can be crucial in getting a job or grant offer.
Know your audience. Adapt the content and your speech to the people you are talking to. Take into consideration their level of expertise but also their predisposition to hear you.
Practice. Try to mimic the same conditions you will have in the real presentation. Ask friends or colleagues to give you feedback. Always test the technical aspects before the seminar, such as laptop, slideshow, sound, projectors, etc. Be in the seminar room ahead of schedule. For online meetings, make sure your camera and microphone are working properly before the seminar. Adjust your camera to be at the same height of your face and avoid “overzooming” it in your face. For these meetings, find a quiet room with enough light and no distractions in the background.
Speak slowly and loudly. Prepare very well the beginning of your talk, since a good start will relax you and the rest will flow with ease. Also, know where the “weaknesses” of your work are and prepare for potential tricky questions. It helps you to remain calm and sound more confident. If needed ask for a microphone. Spend time introducing and motivating the work your describing, Tell the audience what you’re doing and why it’s important that they should care.
Keep it simple I. Too many slides will make the flow of the presentation too fast for the audience to follow. Too many topics on one slide will make your message less clear. A simple rule is to have one idea per slide, and never have more than one slide per minute. Slides are meant as a means of supporting what you’re saying, they are not the talk.
Keep it simple II. Avoid equations and technicalities at all costs. Do not explain every detail of your work, even if some of it mentioned in your slides. Do not be afraid to oversimplify something if you’re having problems communicating your message in a short time. This will give room for “easy” questions where you can develop these more complicated ideas further.
Be concise. Select 2 or 3 main points and reinforce them throughout the presentation (particularly in longer talks). This helps the audience keep track of your talk.
Be consistent. Find a template and stick to it. Don’t use different background colors or change font from slide to slide. Use at most two fonts in your presentation. The font size should be large enough for it to be readable at the back of the room.
Be spare. Too many colors can be distracting. Use two or at most three-color scheme. Use contrasting colors for text and background. For example, use a light colored font on a dark background or dark fonts on a light background. Avoid patterned backgrounds, they reduce readability. Go easy on slide transitions and sound effects.
Give credit. For heaven’s sake, always acknowledge the author of images, plots or results that you use. Check if you’re allowed to use it. Just because you found it online, doesn’t mean it’s up for grabs.
Be thoughtful with the use of images. Use good quality images and plots. Make sure the presentation is aesthetically pleasant.
Engage with the audience and be inclusive. Don’t turn your back to your audience while you speak, it makes you look insecure and it draws a schism between you and the audience. If giving an online seminar, turn the camera on and show your face. It humanizes the experience and helps to keep your audience engaged. Avoid the use of rhetorical questions and exclusion sentences such as “as we all know...” or ”it is a well-known fact...”. There might be someone in the room who actually does not know. In online seminars, it’s ok to pause a few times to ask if anyone has questions. If you feel that no question is coming, move on. Awkward silences break the pace of the talk. It might be useful to coordinate with the seminar organizer on how to keep track of questions and organize these moments.
Respect the allotted time. It is extremely impolite, and annoying for the audience, to have a speaker going beyond their time slot. A well-planned talk is also a show of respect to the next speaker and to the audience.
Applications
To get a career in academia you need a job. To get a job, you need to apply for it. Applying for jobs and grants is an essential part of the life of a researcher. Below, there’s a few tips to help you guide you through this process. Some of them are just common sense, but you may find them useful nonetheless.
Again: Work, work, work. This is by far the most important aspect. Do relevant research. Valuable research is not just about solving problems but about solving important problems. After 2 years on your PhD, you should be independent and tackle questions you find the most pertinent for your career.
Showcase your work. After getting the work done, you need to tell people about it. People need to recognize you by your track record. Personal contact with colleagues (and potential future employers) is a key factor. Don’t stick to your department or university. Engage colleagues in other institutions and countries. Make your talks splendid, be enthusiastic about what you do. Conferences/workshops are great but departmental seminars are where you have the best chance to impress someone. Use these opportunities to mingle with people.
Reach out. Scientific outreach is not only a way to give back to the society. It’s also an opportunity to test and improve communication skills. Sometimes, having to explain your work to a lay audience can help you to have a broader view of science.
Big Science Collaborations. These are useful and important to get challenging work done. Do not think of them as publication machines and do not build a CV based exclusively on publications with hundreds of authors. The community knows exactly who had an important contribution in this kind of publications.
Know when to stop. This is an extreme option, but it needs to be considered. A career in science is not suited nor possible for everyone. If you’re unhappy or haven’t got any job offers, consider looking beyond academia.
Timescales. Depending on where you are applying to, start preparing applications a year in advance. This is a crucial time to be visible. Book departmental seminars, visit other groups, register in conferences, start new collaborations, ask around for opportunities.
Luck Factor. You will always need to be lucky in life.
Curriculum Vitae. A strong and concise CV is important. Update it regularly. Include a list of your publications. Do remember that a CV is just a summary of your career so far, in the end while having a good CV helps, it’s the body of work that counts.
Research Statement. The length/format depends on the type of grant/fellowship/position you are applying to. Again, while a strong research statement in certainly important, no one will hire you solely based on it. Find out who you would be working with and on which topic, and adapt the research statement accordingly. State your research interests but be careful to not sound too narrow, show you are willing to explore different research directions.
Recommendations. Reference letters have to be extremely strong and you should your referees if they are willing to write such a strong letter. Do not ask someone to write you a letter just because he/she is famous or more experienced. The people with whom you have worked the closest are more capable to transmit good information about you. Ask them well in advance so they have enough time. You will usually need 2 or 3 referees.
Useful links where jobs are posted regularly:
Hyperspace (GR focus)
Academic Jobs Online (US centric, but extensive)
InspireJobs (High energy physics focus)
AAS (Astro focus)
DGrav (GR focus)
Mathjobs
Website from Leuven
La Caixa Fellowship
Newton International Felllowship (UK)
Royal Astronomical Society (UK)
We also encourage you to search for other ways of looking at life in academia and beyond. Check, for example, http://gmunu.mit.edu/student/
Lectures by David Pereniguez for a PhD course on spinors in GR at the University of Perugia:
PhD Theses
A. Foschi.The Galactic Center: A Testing Ground for Dark Matter and..., 2024.
F. Duque.Gravitational Waves and the Galactic Potential, 2023.
A. Giannakopoulos. Characteristic Formulations of General Relativity and..., 2022.
I. Suárez.Critical Phenomena in Gravitational Collapse, 2022.
L. Annulli.Challenging Theories of Gravitation..., 2021.
R. Vicente. The Gravity of Classical Fields, 2021.
F. Hedja. Energy Extraction from Black Holes, 2019.
M. Ferreira. Scalar field Effects on the Motion of Stars, 2019.
K. Destounis. Dynamical Behavior of Black-hole Spacetimes, 2019.
P. Cunha.Shadows and Gravitational Lensing of Black Holes..., 2019.
C. Macedo. Compact Objects in General Relativity and Beyond, 2016.
R. Brito. Fundamental Fields Around Compact Objects...,2016.
M. Zilhão. New frontiers in Numerical Relativity, 2012.
H. Witek. Black Hole Dynamics in Generic Spacetimes, 2012.
Master Theses
R. F. Pinto. The Cylinder at Spatial Infinity and Asymptotic Charges, 2023.
R. Pinto Santos.Characteristic Critical Collapse with Null Infinity, 2023.
J. S. dos Santos. Radiation Reaction in Magnetized Black Holes, 2023.
J. Patiño. Numerical Relativity in Axisymmetry, 2023.
T. Zhou.Quantifying the Nature of Compact Objects, 2023.
R. Arana.Tidal Deformability of Gravitational Atoms, 2023.
I. A. Rainho. Linearized General Relativity on Hyperboloidal Slices, 2022.
D. A. Piçarra. Accretion Disks Around Compact Objects, 2022.
D. C. Ribeiro.Analogue Binaries and Superradiance, 2022.
T. V. Fernandes. Vector Fields and Black Holes, 2020.
M. Boškovic.Parametric-Resonance Based Phenomenology of..., 2019.
G. Castro. Gravitational Waves and Massive Gravitons, 2018.
R. Franco. Magnus Effect in General Relativity, 2018.
M. Correia.Characterization of Echoes: Toy Models and..., 2018.
S. Freitas.Acoustic Black Holes and Superresonance Mechanisms, 2017.
G. Raposo. Relativistic Tidal Love Numbers: Tests of..., 2016.
R. Vicente. Superradiance of Bosonic Fermion Condensates, 2016.
M. Duarte. Bosonic Stars: Scalar and Vector Field..., 2016.
J. L. Rosa. Superradiant Amplification by Stars and Black Holes, 2015.
J. Lopes. Stability of AdS, 2014.
J. Rico.The Kerr Black Hole Hypothesis: A Review..., 2013.
I. Carucci. Matter Around Black Holes: Testing Scalar-Tensor..., 2013.
P. Luz. Efeitos de Auto-interação na Dinâmica de um Corpo..., 2012.
R. Brito. Dynamics Around Black Holes: Radiation Emission..., 2012.
M. Marques. Acoustic Black Holes and Superresonance Mechanism, 2011.
M. Lemos. Approximation Methods in the Study of Gravitational-Wave..., 2010.
The oscillation modes of black holes, called quasinormal modes, are fundamental quantities in gravitational-wave astronomy, no-hair tests of General Relativity and even in a gauge-gravity duality context. Here you can find useful material for research, including comprehensive data for the quasinormal mode spectrum of Kerr black holes, and powerful yet simple routines to compute them. The data and routines are freely available, but we would appreciate if you reference the original work.
| RINGDOWN DATA | ||
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| Description | References | Download |
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Frequency basis for parametrized black hole QNMs |
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Schwarzschild QNMs Format: 2MωR, 2MωI, error, n |
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Kerr QNM frequencies (Gravitational s=-2) |
l=2 tar file |
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Kerr QNM frequencies (Electromagnetic s=-1) |
l=1 tar file |
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Kerr QNM frequencies (Scalar s=0) |
l=0 tar file |
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KN QNM frequencies (Gravitational modes) |
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QNM Excitation factors (scalar, vectors and tensors) |
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Fits to Kerr QNMs |
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QNM frequencies with 20-digit precision |
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Kerr QNM frequencies and excitation factors |
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| RINGDOWN ROUTINES | ||
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| Description | References | Download |
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Computation of Kerr QNMs with Leaver’s method |
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Computation of Regge - Wheeler and Zerilli equation using Mathematica and xTensor |
Regge & Wheeler, Phys. Rev. 108, 1063 (1957) |
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Computation of QNMs with direct integration |
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Computation of SAdS QNMs using power-series methods |
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QNMs of RNdS black holes |
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Proca fields on a Kerr BH slow-rotation approximation |
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QNMs of Kerr-Newman BHs slow-rotation approximation |
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Massive spin-2 fluctuations slow-rotation approximation |
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Solves the eigenspectrum of unstable modes of a Kerr BHunder massive scalar perturbations through Leaver's continued fraction method |
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Computation of the QNMs of EDGB black hole |
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Superradiant Bounds on Ultralight Fields
See Brito, Cardoso and Pani, Superradiance, Lectures Notes in Physics 906 (2020).
| SUPERRADIANT BOUNDS ON ULTRALIGHT FIELDS | ||
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| Excluded Region (in eV) | Source | References |
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5.2x10-13 < mS <6.5x10-12 * |
Direct bounds from absence of spin in Cyg X-1 |
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3.8×10−14 < mS < 2x3.4×10−11 |
Indirect bounds from BH mass-spin measurements |
arXiv:1411.2263 |
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1.2×10−13 < mS < 1.8×10−13 |
Null results from blind all-sky searches for continuous GW signals |
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6.4×10−13 < mS < 8.0×10−13 |
Null results from searches for continuous GW signals from Cygnus X-1 |
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2.0×10−13 < mS < 3.8×10−13 |
Negative searches for a GW background |
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5×10−13 < mS < 3×10−12 |
Bounds from pulsar timing |
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2.9×10−21 < mS < 4.6×10−21 |
Bounds from mass and spin measurement of M87 with EHT |
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* See Brito, Cardoso and Pani, Superradiance, Lectures Notes in Physics 906 (2020).
Amplification Factors in Kerr And Routines
Superradiant amplification of massless waves scattering off Kerr black holes is an important phenomena in curved spacetime. Details of the process can be found in an outstanding work by Press and Teukolsky (ApJ193, 443 (1974)), but extensive tables and routines to compute them are lacking. We provide here such data. The routines are freely available, but we would appreciate if you refer to the original work.
| AMPLIFICATION FACTORS DATA AND ROUTINES | ||
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| Amplification Factors Data | References | Download |
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Amplification factors of massless fields |
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Amplification Factors Routines |
References |
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Amplification factors of the superradiant |
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Amplification factors of the superradiant |
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Cardoso et al. Metric functions and perturbations equations for black hole solutions in Effective Field Theories. Phys. Rev. Lett. 121: 251105 (2018). [arxiv:1808.08962]
Readme (Rich Text Format)
Effective Potencials Webpage (Mathematica Notebook)
EFT BH Geodesics (Mathematica Code)
EFT BH Metric (Mathematica Code)
Solutions of Einstein's equations can be obtained analytically in a handful of cases. Generically, it requires sophisticated techniques. Here we show some simple routines (under the form of notebooks or C++ routines) to compute (stationary) hairy black hole solutions in massive theories of gravity and static neutron star structure in alternative theories of gravity. Finally, we also make available a 1+1 code to evolve a spherically symmetric, scalar wavepacket in AdS spacetimes. The routines are freely available, but we would appreciate if you reference the original work.
| NONLINEAR SOLUTIONS | ||
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| Description | References | Download |
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Hairy BHs in massive gravity |
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NSs in scalar-tensor gravity |
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Scalar Field Collapse in AdS |
Lopes, Okawa & Cardoso |
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Kerr black holes with scalar hair |
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(i) computes and solves Einstein's equations |
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| Boson Stars | ||
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| Description | References | Download |
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Spherically symmetric boson stars |
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Tidal Love numbers for exotic compact objects (boson stars, gravastars, wormholes, mirrors).
| TIDAL LOVE NUMBERS | ||
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| Description | References | Download |
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Love numbers of ECOs. |
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Basis for parametrized black hole TLNs. |
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Radiation from Plunging Particles
Gravitational radiation from point-like particles plunging into black holes has a very long history, and is known to reproduce accurately even highly non-linear processes like equal mass black hole collisions. We will gather here some Mathematica routines to compute gravitational radiation from the plunging of particle into black holes, both in GR and in some modified theories of gravity.
| RADIATION FROM PLUNGING PARTICLES | ||
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| Description | References | Download |
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Radiation from a pointlike particle plunging into a Reissner-Nordstrom black hole. |
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Radiation from a pointlike particle plunging into a EDGB black hole. |
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Perturbation of Schwarzschild black hole in dRGT massive gravity. |
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Gravitational Waves from Boson Clouds
Here you can find routines that can be used to compute the flux in gravitational waves emitted by a scalar cloud around a Kerr black hole. Some computations make use of the Black Hole Perturbation toolkit (bhptoolkit.org). We also use results from arXiv:0306120, arXiv:0705.2880 and arXiv:1312.2326. The data generated by this routine served as input for the python package gwaxion (pypi.org/project/gwaxion).
| GRAVITATIONAL WAVES FROM BOSON CLOUDS | ||
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| Description | References | Download |
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Computation of gravitational-wave flux from a scalar cloud. |
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Scalar and gravitational fluxes from EMRIs in scalar environments. |
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EMRIs in Astrophysical Environments
Here you can find routines to compute the radiation emitted by an extreme-mass-ratio inspiral in spherically-symmetric, non-vacuum black-hole spacetimes. We specialize to the case of a black hole within a halo of matter based on the solution found in arXiv:2109.00005, but you can adapt it to other backgrounds.
| EMRIs in Astrophysical Environments | ||
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| Description | References | Download |
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Time-domain code |
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Frequency-domain code |
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Video Files
Parasitic black holes. The swallowing of a fuzzy dark matter soliton. Time evolution of BH mass (top panel), scalar field (bottom left), and energy flux (bottom right). Initial boson star mass is 15 times heavier than initial black hole mass. Initial boson star size is 600 times larger than black hole radius. arXiv:2207.09469v1.
Piercing of boson stars by a black hole (I). A black hole of unit mass colliding with a boson star of mass 0.53. The collision happens at 50% the speed of light. arXiv:2206.00021.
Piercing of boson stars by a black hole (II). A black hole of unit mass colliding with a boson star of mass 0.53. The collision happens at 50% the speed of light. Right panel: a black hole of mass 0.1 colliding with a boson star of mass 0.53. The collision happens at 50% the speed of light. arXiv:2206.00021.
High energy black hole collisions. The collision of two boosted black holes (v=0.75c in the center of mass frame), with a finite impact parameter in asymptotically flat spacetime. About 24% of the center of mass frame can be released as radiation, for this collision. The final hole is nearly maximally spinning. The intensity of the color refers to the amplitude of the gravitational waves as measured by Ψ4. arXiv:0907.1252.
Black holes in a box. The inspiral and coalescence of two black holes, with total mass M, inside a confining box of radius 48 M. Out- and in-going waves are measured respectively by Ψ4 and Ψ0. arXiv:1004.4633.
Black hole bombs I: Scalar fields. The time evolution of a massive scalar field around a highly spinning black holes. The scalar field is initially in a bound state, and continues to be for thousands of orbital periods. Colors depict field intensity. arXiv:1212.0551.
Black hole bombs II: Vector fields. The time evolution of a massive vector field around a highly spinning black holes. The vector field is initially a generic gaussian. Colors depict field intensity. arXiv:1212.0551.
Black hole collisions in de Sitter spacetime. Two black holes of sufficiently large mass in de Sitter spacetime would, upon merger, give rise to too large a black hole to fit in its cosmological horizon, resulting in a naked singularity. We here test such a configuration. Even though the initial separation is very small, we find that the holes move away from each other, with a proper separation increasing as the simulation progresses. arXiv:1204.2019.
Bursts of light from axion clouds (I). The evolution of an axion Phi of mass mu=0.2 and of the electromagnetic scalar E2-B2 in the background of a Kerr BH (a=0.5). The initial axion configuration describes a cloud around a spinning black hole, grown by superradiance.
When superradiance is turned off and the initial amplitude of the axion is small, any vector perturbation dies off quickly. arXiv:1811.04950.
Bursts of light from axion clouds (II). When superradiance is turned off and the initial amplitude of the axion is large, an instability is triggered and gives rise to a EM burst. arXiv:1811.04950.
Bursts of light from axion clouds (III). When superradiant growth is included, even a small initial axion amplitude eventually grows large and triggers EM bursts, blasts of laser-like electromagnetic radiation. This blasts lowers the axion to sub-critical values, until superradiance dominates again. arXiv:1811.04950.
Turbulent accretion disk around a supermassive black hole (I). The turbulent gas flow stochastically excites the quasinormal modes of the central black hole which leads to gravitational wave emission.
Turbulent accretion disk around a supermassive black hole (II). See description above.
Audio Files
Echoes from quasicircular inspiral of a mass ratio 1:100 binary. Massive object is a ClePhO (horizonless object). arXiv:1602.07309; arXiv:1608.08637; arXiv:1904.05363.
Audio data:
audio q=[1 .. 100] quasi-circular echoes;
wave 22, Schwarzschild Radius 100