95 pages, 11 figures; a nomenclature for the braneworld BH conjecture corrected, references added and updated; Invited review article to the Focus Issue on "Black holes and fundamental fields" published in Classical and Quantum Gravity
General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is 4 dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar-tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole-based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.
We present a new set of analytic solutions of general relativity with a negative cosmological constant, which describe black strings and black p-branes in arbitrary number of dimensions, $D$. The solutions are supported by minimally coupled, free scalar fields, carrying finite energy density.
Fermionic Love of Black Holes in General Relativity
Indian Association for the Cultivation of Science（印度科学培养协会）；The Ohio State University（俄亥俄州立大学）；“Sapienza” Università di Roma（罗马智慧大学）；Sezione INFN Roma1（意大利国家核物理研究所罗马第一分部）
A general Hamiltonian approach to black hole thermodynamics is used to study entropy and conserved charges for Kerr-AdS solutions in general relativity. These thermodynamic variables are first consistently defined by choosing suitable boundary conditions, and then, they are shown to satisfy the first law of black hole dynamics
It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.
Black hole thermodynamics of the Kerr-AdS spacetime in three-dimensional general relativity is analyzed using a Hamiltonian approach. The values of the conserved charges and entropy, obtained by a proper treatment of the AdS asymptotic conditions, are shown to satisfy the first law of black hole dynamics.
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This review presents a comprehensive survey of the various versions of the first law and second law of black hole mechanics in general relativity and beyond. The emphasis is to understand how these laws can constrain the physics beyond general relativity.
Recent nonlinear completions of Fierz-Pauli theory for a massive spin-2 field include nonlinear massive gravity and bimetric theories. The spectrum of black-hole solutions in these theories is rich, and comprises the same vacuum solutions of Einstein's gravity enlarged to include a cosmological constant. It was recently shown that Schwarzschild (de Sitter) black holes in these theories are generically unstable against spherical perturbations. Here we show that a notable exception is partially massless gravity, where the mass of the graviton is fixed in terms of the cosmological constant by μ^2…
Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarise the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic $D$-dimensional spacetimes.
Gravitational waves from the coalescence of two black holes carry the signature of the strong field dynamics of binary black holes. In this work we have used numerical relativity simulations and post-Newtonian theory to investigate this dynamics. Post-Newtonian theory is a low-velocity expansion that assumes the companion bodies to be point-particles, while numerical relativity treats black holes as extended objects with horizons and fully captures their dynamics. There is a priori no reason for the waveforms computed using these disparate methods to agree with each other, especially at late t…
The first regular exact black hole solution in General Relativity is presented. The source is a nonlinear electrodynamic field satisfying the weak energy condition, which in the limit of weak field becomes the Maxwell field. The solution corresponds to a charged black hole with |q| \leq 2 s_c m \approx 0.6 m, having the metric, the curvature invariants, and the electric field regular everywhere.
We perturbatively construct asymptotically $\mathbb{R}^{1,3}\times\mathbb{T}^2$ black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.
Einstein-Maxwell equations with a cosmological constant are analyzed in a four dimensional stationary spacetime admitting in addition a two dimensional group $G_2$ of spatial isometries. Charged rotating open and closed black string solutions are found.
We consider a system of black holes -- a simplest substitute of a system of point particles in the mechanics of general relativity -- and try to describe their motion with the help of entropic action: a sum of the areas of black hole horizons. We demonstrate that such description is indeed consistent with the Newton's laws of motion and gravity, modulo numerical coefficients, which coincide but seem different from unity. Since a large part of the modern discussion of entropic reformulation of general relativity is actually based on dimensional considerations, for making a next step it is cruci…
Einstein's theory of General Relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and observations of binary pulsars. Thanks to a new generation of observational facilities, the past 5 years have seen remarkable changes in this field and there are now numerous efforts for testing General Relativity in the strong field regime with black holes and neutron stars using different techniques. Here I will review the work of my group at Fudan University devoted to test General Relativity with bl…
Schwarzschild black-hole immersed in an electric or magnetic background in Entangled Relativity
Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur（阿耳特弥斯，蔚蓝海岸大学，法国国家科学研究中心，蔚蓝海岸天文台）；Bureau des Affaires Spatiales（空间事务局）；Departament de Física Quántica i Astrofísica (FQA), Universitat de Barcelona (UB)（巴塞罗那大学量子物理与天体物理学系）
We propose a new test of strong-field general relativity (GR) based on the universal interferometric signature of the black hole photon ring. The photon ring is a narrow ring-shaped feature, predicted by GR but not yet observed, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. We show that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefo…
For the celebrations of the 100 years of the observations undertaken by Eddington at the island of Principe and collaborators at Sobral during a total solar eclipse in May 29, 1919, which have confirmed Einstein's theory of general relativity through the deflection of the incoming light from distant stars due to the spacetime curvature caused by the Sun, we highlight the main aspects of the theory, its tests and applications, focusing on some of its outstanding consequences. These are black holes, the object par excellence of general relativity, and gravitational waves, the gravitational probe…
We present a general procedure for constructing exact black hole solutions with electric or magnetic charges in General Relativity coupled to a nonlinear electrodynamics. We obtain a variety of two-parameter family spherically symmetric black hole solutions. In particular, the singularity at the central of the space-time can be cancelled in the parameters space and the black hole solutions become regular everywhere in the space-time. We study the global properties of the solutions and derive the first law of thermodynamics. We also generalize the procedure to include a cosmological constant an…
Einstein's theory of General Relativity was proposed over 100 years ago and has successfully passed a large number of observational tests in weak gravitational fields. On the contrary, the strong field regime is still largely unexplored. Astrophysical black holes are ideal laboratories for testing gravity in the strong field regime. Here I will briefly review the current efforts of my group to test the strong gravitational field around black holes using X-ray data from NuSTAR, RXTE, Suzaku, and XMM-Newton.
Einstein's theory of General Relativity predicts that the spacetime metric around astrophysical black holes is described by the Kerr solution. In this work, we employ state-of-the-art in relativistic reflection modeling to analyze a selected set of NuSTAR spectra of Galactic black holes to obtain the most robust and precise constraints on the Kerr black hole hypothesis possible today. Our constraints are much more stringent than those from other electromagnetic techniques, and with some sources we get stronger constraints than those currently available from gravitational waves.
Measurements of black-hole spins are of crucial importance to fulfill the promise of gravitational-wave astronomy. On the astrophysics side, spins are perhaps the cleanest indicator of black-hole evolutionary processes, thus providing a preferred way to discriminate how LIGO's black holes form. On the relativity side, spins are responsible for peculiar dynamical phenomena (from precessional modulations in the long inspiral to gravitational-wave recoils at merger) which encode precious information on the underlying astrophysical processes. I present some examples to explore this deep and fascin…
We describe a simple implementation of black hole excision in 3+1 numerical relativity. We apply this technique to a Schwarzschild black hole with octant symmetry in Eddington-Finkelstein coordinates and show how one can obtain accurate, long-term stable numerical evolutions.
The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. The past five years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and mm Very Long Baseline Interferometry observations. Here I summarize the state-of-the-art of the tests of General Relativity with black hole X-ray data, discussing its recent progress and future development…
In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole -- for which the solution of entangled relativity and a dilaton theory agree -- as well as the case of a pure radiation -- for which the solution of entangled r…
We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on some developments that took place within the "Numerical Relativity and High Energy Physics" network, a Marie Curie IRSES action that we coordinated, namely: spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar-tensor gravity, superradiant instabilities and hairy black hole solutions in Einstein's gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog grav…
We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of {\it Modified Generalized Uncertainty Principle} suggested by {\it Doubly Special Relativity}.
Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the capabilities of numerical relativity codes, recent physical results obtained from simulations, and improvements to the methods used to evolve and analyse binary black hole spacetimes.
The ring-down phase of black-hole perturbations is governed by the Quasi-Normal modes (QNM) and offer valuable insight into the nature of the objects emitting them. In General relativity, we identify a dimensionless parameter that can estimate the charge of a black-hole from the energetics of quasi-normal modes. We then extend the analysis for f(R) theories of gravity. Using Isaacson's prescription to modified theories of gravity, we obtain an accurate and robust method to estimate the difference in the radiated energies in the scalar and vector modes due to modifications to general relativity…
Although the Kerr solution is common to many gravity theories, its perturbations are different in different theories. Hence, perturbed Kerr black holes can probe deviations from General Relativity.
We show that there is an inconsistency in the class of solutions obtained in Phys. Rev. D {\bf 95}, 084037 (2017). This inconsistency is due to the approximate relation between lagrangian density and its derivative for Non-Linear Electrodynamics. We present an algorithm to obtain new classes of solutions.
The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. Recently, there have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and mm Very Long Baseline Interferometry observations. Here we summarize the state-of-the-art of the tests of General Relativity with black hole X-ray data, discussing its recent progress and future developments.
We study 4-dimensional non-charged and charged spherically symmetric spacetimes in conformal teleparallel equivalent of general relativity. We apply the gravitational field equations in non-charged and charged spacetimes to the diagonal and non-diagonal vierbeins and derive their sets of the non-linear differential equations. It is demonstrated that the Schwarzschild, for the non-charged case, and the Reissner-Nordström, for the charged case, are the only black hole solutions for the spherically symmetric case in the framework of the conformal teleparallel equivalent of general relativity theo…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes theory towards a specific objective: understanding how the combination of extended black objects and ultra-spinning rotation dynamics give rise to black hole topologies that depart from sphericity. The discussion aims to offer a compromise between giving a reasonably wide picture of the area of higher dimensional black holes, while at the same time going into de…
The iron line and the continuum-fitting methods are currently the two leading techniques for measuring black hole spins with electromagnetic radiation. They can be naturally extended for probing the spacetime geometry around black holes and testing general relativity in the strong field regime. In the past couple of years, there has been significant work to use the iron line method to test the nature of black holes. In this Letter, we use the continuum-fitting method and we show its capability of constraining the spacetime geometry around black holes by analyzing 17 RXTE data of the X-ray bina…
I present two results that show that, despite its unusual non-linear form, the phenomenology of entangled relativity remains close to the one of general relativity -- without having any free parameter that can be fine tuned in order to facilitate this. In particular, I present the analytical solutions for spherically charged black-holes, and both the analytical and numerical solutions for neutron stars.
In this paper we study the Hawking radiation in Reissner-Nordstrom and Kerr-Newman black holes by considering the charge to be the function of radial coordinate.
The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first foray into the long time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitably small neighborhood of Minkowskian data. The theorems are general, no symmetry conditions on the initial data being imposed.
A black hole solution of Einstein's field equations with cylindrical symmetry is found. Using the Hamiltonian formulation one is able to define mass and angular momentum for the cylindrical black hole through the corresponding and equivalent three dimensional theory. The causal structure is analyzed. Comments: revised version.
What is going on (as of August 2008) at the interface between theoretical general relativity, string-inspired models, and observational astrophysics? Quite a lot. In this mini-survey I will make a personal choice and focus on four specific questions: Do black holes "exist"? (For selected values of the word "exist".) Is black hole formation and evaporation unitary? Can one mimic a black hole to arbitrary accuracy? Can one detect the presence of a horizon using local physics?
Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this paper, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the nee…
In the presence of compact dimensions massive solutions of General Relativity may take one of several forms including the black-hole and the black-string, the simplest relevant background being R^{3+1} * S^1. It is shown how Morse theory places constraints on the qualitative features of the phase diagram, and a minimalistic diagram is suggested which describes a first order transition whose only stable phases are the uniform string and the black-hole. The diagram calls for a topology changing ``merger'' transition in which the black-hole evolves continuously into an unstable black-string phase…
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for Numerical Relativity, in particular for their use in black hole excision. As an application, we present 3D simulations of a scalar field propagating in a Schwarzschild black hole background.
The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.
In this paper, we review our current efforts to test General Relativity in the strong field regime by studying the reflection spectrum of supermassive black holes. So far we have analyzed 11 sources with observations of NuSTAR, Suzaku, Swift, and XMM-Newton. Our results are consistent with general relativity, according to which the spacetime metric around astrophysical black holes should be well approximated by the Kerr solution. We discuss the systematic uncertainties in our model and we present a preliminary study on the impact of some of them on the measurement of the spacetime metric.
The fundamental role played by black holes in our study of microquasars, gamma ray bursts, and the outflows from active galactic nuclei requires an appreciation for, and at times some in-depth analysis of, curved spacetime. We highlight misconceptions surrounding the notion of coordinate transformation in general relativity as applied to metrics for rotating black holes that are beginning to increasingly appear in the literature. We emphasize that there is no coordinate transformation that can turn the metric of a rotating spacetime into that for a Schwarzschild spacetime, or more generally, t…
We apply common gravitational wave inference procedures on binary black hole merger waveforms beyond general relativity. We consider dynamical Chern-Simons gravity, a modified theory of gravity with origins in string theory and loop quantum gravity. This theory introduces an additional parameter $\ell$, corresponding to the length-scale below which beyond-general-relativity effects become important. We simulate data based on numerical relativity waveforms produced under an approximation to this theory, which differ from those of general relativity in the strongly nonlinear merger regime. We co…
Recently, we have extended the X-ray reflection model relxill to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter $α_{13}$. Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.
Observations of the black hole shadow of supermassive black holes, such as Sagittarius A* at the center of our Milky Way galaxy, allow us to study the properties of black holes and the nature of strong-field gravity. According to the Kerr hypothesis, isolated, stationary, and axisymmetric astrophysical black holes are described by the Kerr metric. The Kerr hypothesis holds in General Relativity and in some modified gravity theories, but there are others in which it is violated. In principle, black hole shadow observations can be used to determine if the Kerr metric is the correct description f…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and characteristic evolution is highlighted, as well as full 3D simulations of colliding and distorted black holes. For true 3D distorted holes, with Cauchy evolution techniques, it is now possible to extract highly accurate, nonaxisymmetric waveforms from fully nonlinear simulations, which are verified by comparison to pertubration theory, and with characteristic techniqu…
Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only be calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists att…
We study a three-parameters family of solutions of the Brans-Dicke field equations. They are static and spherically symmetric. We find the range of parameters for which this solution represents a black hole different from the Schwarzschild one. We find a subfamily of solutions which agrees with experiments and observations in the solar system. We discuss some astrophysical applications and the consequences on the "no hair" theorems for black holes.
