We prove a theorem that characterizes a large family of non-static solutions to Einstein equations, representing, in general, spherically symmetric Type II fluid. It is shown that the best known dynamical black hole solutions to Einstein equations are particular cases from this family. Thus we extend a recent work of Salgado \cite{ms} to non-static case. The spherically symmetric static black hole solutions, for Type I fluid, are also retrieved.
We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EMd equations are completely integrable. We also develop a solution generating method for explicit construction of exact EMd solutions from known exact solutions of 5D vacuum Einstein equations with considered symmetries. We derive explicitly the rotating dipole black ring solutions as a particular application of the…
The Hawking radiation is considered as a quantum tunneling process, which can be studied in the framework of the Hamilton-Jacobi method. In this study, we present the wave equation for a mass generating massive and charged scalar particle (boson). In sequel, we analyze the quantum tunneling of these bosons from a generic 4-dimensional spherically symmetric black hole. We apply the Hamilton-Jacobi formalism to derive the radial integral solution for the classically forbidden action which leads to the tunneling probability. To support our arguments, we take the dyonic Reissner-Nordström black ho…
Multi-black hole solutions play a relevant role both from the theoretical and the phenomenological point of view. In this Thesis, we construct some regular multi-black hole spacetimes in pure Einstein's General Relativity with the aid of solution generating techniques. We begin with a perspective on the history of solution generating techniques, and then we explain in detail the Ernst formalism and the inverse scattering method. These are the techniques that are applied in the rest of the Thesis. Subsequently, we construct multi-black hole solutions embedded in an external gravitational field:…
Recently we suggested a solution generating technique for five-dimensional supergravity with three Abelian vector fields based on the hidden SO(4,4) symmetry of the three-dimensionally reduced theory. This technique generalizes the $G_{2(2)}$ generating technique developed earlier for minimal 5D supergravity (A. Bouchareb, G. Clément, C-M. Chen, D. V. Gal'tsov, N. G. Scherbluk, and Th. Wolf, Phys. Rev. D {\bf 76}, 104032 (2007)) and provides a new matrix representation for cosets forming the corresponding sigma-models in both cases. Here we further improve these methods introducing a matrix-va…
This paper exploits the power of the Cayley-Dickson algebra to generate stationary rotating black hole solutions in one fell swoop. Specifically, we derive the nine-dimensional Myers-Perry solution with four independent angular momenta by using the Janis-Newman algorithm and Giampieri's simplification method, exploiting the octonion algebra. A general formula relating the dimension of the Cayley-Dickson algebra with the maximum number of angular momenta in each dimension is derived. Finally, we discuss the cut-off dimension for using the Cayley-Dickson construction along with the Janis-Newman …
A solution generating technique is developed for D=5 minimal supergravity with two commuting Killing vectors based on the $G_2$ U-duality arising in the reduction of the theory to three dimensions. The target space of the corresponding 3-dimensional sigma-model is the coset $G_{2(2)}/(SL(2,R)\times SL(2,R))$. Its isometries constitute the set of solution generating symmetries. These include two electric and two magnetic Harrison transformations with the corresponding two pairs of gauge transformations, three $SL(2,R) S$-duality transformations, and the three gravitational scale, gauge and Ehle…
In this paper we construct the BPS black hole generating solution of toroidally compactified string (and M) theory, giving for it both the macroscopic and microscopic description. Choosing a proper U-duality gauge the latter will be given by a bound state made solely of D-branes. The axionic nature of the supergravity solution will be directly related to non-trivial angles between the constituent D-branes (type IIB configuration) or, in a T-dual gauge, to the presence of magnetic flux on constituent D-brane world volumes (type IIA configuration). As expected, the four dimensional axion fields …
Starting with a Zipoy-Voorhees line element we construct and study the three parameter family of solutions describing a deformed black string with arbitrary tension.
The Newman-Janis and Giampieri algorithms are two simple methods to generate stationary rotating black hole solutions in four dimensions. In this paper, we obtain the Mayers-Perry black hole from the Schwartzchild solution in five dimensions using quaternions. Our method generates the Mayers-Perry black hole solution with two angular momenta in one fell swoop.
In this review we present the most general form of the Janis--Newman algorithm. This extension allows to generate configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański-Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.
New coordinates are given which describe non-degenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.
Solutions-generating methods based on field redefinitions, such as conformal mapping, play an important role in investigating exact solutions in modified gravity. In this work, we explore the possibility to use disformal field redefinitions to investigate new regions of the solution space of DHOST theories. The crucial ingredient is to find suitable seed solutions to generate new exact ones for DHOST theories. We first consider a seed solution of the Einstein-Scalar system describing a naked singularity. Under suitable assumptions, we derive a no-go result showing that no black hole solution c…
In this paper, we have presented an algorithm to generate various black hole solutions in general relativity and alternative theories of gravity. The algorithm involves few dimensional parameters that are assigned suitable values to specify the required black hole.
We construct dynamical black ring solutions in the five dimensional Einstein-Maxwell system with a positive cosmological constant and investigate the geometrical structure. The solutions describe the physical process such that a thin black ring at early time shrinks and changes into a single black hole as time increase. We also discuss the multi-black rings and the coalescence of them.
We show that the static and asymptotically flat black hole spacetime is unique to be Schwarzschild spacetime in the dynamical Chern-Simons gravity. In addition, we show that the strictly static spacetimes should be the Minkowski spacetime.
We extend the standard Kerr-Schild solution generating method to higher order scalar tensor theories that are shift-invariant for the scalar field. Certain degeneracy conditions, crucial for the absence of Ostrogradski ghosts, are found to be required for the validity of the Kerr-Schild ansatz while on the other hand, theories with no parity symmetry are excluded from the solution generating method. The extended Kerr-Schild symmetry turns out to be a very useful tool to easily construct black hole solutions from simple seed configurations. In particular, the generating method developed is adap…
We study the dynamical behavior of the BTZ (Banados-Teitelboim-Zanelli) black hole with the low-energy string effective action. The perturbation analysis around the BTZ black hole reveals a mixing between the dilaton and other fields. Introducing the new gauge (dilaton gauge), we disentangle this mixing completely and obtain one decoupled dilaton equation. We obtain the decay rate $Γ$ of BTZ black hole.
In a recent paper we have given the macroscopic and microscopic description of the generating solution of toroidally compactified string theory BPS black holes. In this note we compute its corresponding microscopic entropy. Since by definition the generating solution is the most general solution modulo U-duality transformations, this result allows for a description of the fundamental degrees of freedom accounting for the entropy of any regular BPS black holes of toroidally compactified string (or M) theory.
Scalar fields coupled to the Gauss-Bonnet invariant can undergo a tachyonic instability, leading to spontaneous scalarization of black holes. Studies of this effect have so far been restricted to single black hole spacetimes. We present the first results on dynamical scalarization in head-on collisions and quasicircular inspirals of black hole binaries with numerical relativity simulations. We show that black hole binaries can either form a scalarized remnant or dynamically descalarize by shedding off its initial scalar hair. The observational implications of these findings are discussed.
We develop generating technique for solutions of $U(1)^3 5D$ supergravity via dimensional reduction to three dimensions. This theory, which recently attracted attention in connection with black rings, can be viewed as consistent truncation of the $T^6$ compactification of the eleven-dimensional supergravity. Its further reduction to three dimensions accompanied by dualisation of the vector fields leads to 3D gravity coupled sigma model on the homogeneous space $SO(4,4)/SO(4)\times SO(4)$ or $SO(4,4)/SO(2,2)\times SO(2,2)$ depending on the signature of the three-space. We construct a $8\times 8…
In this article we extend to higher dimensional space-times a recent theorem proved by Salgado which characterizes a three-parameter family of static and spherically symmetric solutions to the Einstein Field Equations. As it happens in four dimensions, it is shown that the Schwarzschild, Reissner-Nordstrom and global monopole solutions in higher dimensions are particular cases from this family.
We study the dynamical evolution of a massless scalar perturbation in the Hořava-Lifshitz black-hole spacetimes with the coupling constants $λ={1/3}$, $λ={1/2}$ and $λ=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Hořava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Hořava-Lifshitz gravity.
We discuss the Hawking radiation in the Higgs-Yukawa system and we show dynamical formation of a spherical domain wall around the black hole. The formation of the spherical wall is a general property of the black hole whose Hawking temperature is equal to or greater than the energy scale of the system. The formation of the electroweak wall and that of the GUT wall are shown as realistic cases. We also discuss a phenomenon of the spontaneous charging-up of the black hole. The Hawking radiation can charge-up the black hole itself by the charge-transportation due to the spherical wall when C- and…
We construct a black-hole spacetime which includes the running of the gravitational coupling in a self-consistent way. Starting from a classical Schwarzschild black hole, the backreaction effects produced by the running Newton's coupling are taken into account iteratively. The sequence, described by a simple recurrence relation, flows towards a self-consistent solution that can be derived analytically. As a key result, if the gravitational renormalization group flow attains a non-trivial fixed point at high energies, the sequence converges to a "renormalized" black-hole spacetime of the Dymnik…
We introduce, in a systematic way, a set of generating functions that solve all the different combinatorial problems that crop up in the study of black hole entropy in Loop Quantum Gravity. Specifically we give generating functions for: The different sources of degeneracy related to the spectrum of the area operator, the solutions to the projection constraint, and the black hole degeneracy spectrum. Our methods are capable of handling the different countings proposed and discussed in the literature. The generating functions presented here provide the appropriate starting point to extend the re…
We construct generating solutions for general D-dimensional ($4 \le D \le 9$) rotating, electrically charged, black holes in the effective action of toroidally compactified heterotic (or Type IIA) string. The generating solution is parameterized by the ADM mass, two electric charges and $[{D-1}\over 2]$ angular momenta (as well as the asymptotic values of one toroidal modulus and the dilaton field). For $D \ge 6$, those are generating solutions for {\it general} black holes in toroidally compactified heterotic (or type IIA) string. Since in the BPS-limit (extreme limit) these solutions have si…
We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. Finally, we test two proposals for dynamical en…
We consider an augmented Einstein-Maxwell-scalar model including an axionic-type coupling between the scalar and electromagnetic field. We study dyonic black hole solutions in this model. For the canonical axionic coupling emerging from high energy physics, all charged black holes have axion hair. We present their domain of existence and investigate some physical properties. For other axionic-type couplings, two classes of black hole solutions may co-exist in the model: scalar-free Reissner-Nordström black holes and scalarised black holes. We show that in some region of the parameter space, th…
Hidden simplicity in the scattering for neutron stars and black holes
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）
We study massive scalar field perturbation on Kerr black holes in dynamical Chern-Simons gravity by performing a $(2+1)$-dimensional simulation. Object pictures of the wave dynamics in time domain are obtained. The tachyonic instability is found to always occur for any nonzero black hole spin and any scalar field mass as long as the coupling constant exceeds a critical value. The presence of the mass term suppresses or even quenches the instability. The quantitative dependence of the onset of the tachyonic instability on the coupling constant, the scalar field mass and the black hole spin is g…
Critical gravity is a quadratic curvature gravity in four dimensions which is ghost-free around the AdS background. Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition. In addition, the solution shows that the Wald-Kodama dynamical entropy of a black hole is negative and can decrease. These properties expose the pathological aspects of critical gravity at the non…
We recast the system of Einstein field equations for Locally Rotationally Symmetric spacetimes into an autonomous system of covariantly defined geometrical variables. The analysis of this autonomous system gives all the important global features of the maximal extension of these spacetimes. We conclude that the dynamical system analysis can be a powerful mathematical tool for qualitative understanding of the global structure of spacetimes covariantly, without actually solving the field equations.
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this the…
Recently, a novel kind of scalar wigs around Schwarzschild black holes---scalar dynamical resonance states were introduced in [Phys. Rev. D 84, 083008 (2011)] and [Phys. Rev. Lett. 109, 081102 (2012)]. In this paper, we investigate the existence and evolution of Dirac dynamical resonance states. First we look for stationary resonance states of a Dirac field around a Schwarzchild black hole by using the Schrödinger-like equations reduced from the Dirac equation in Schwarzschild spacetime. Then Dirac pseudo-stationary configurations are constructed from the stationary resonance states. We use th…
We work on the relation between the local thermodynamic instability and the dynamical instability of large black holes in four-dimensional anti-de Sitter space proposed by Gubser and Mitra. We find that all perturbations suppressing the metric fluctuations at linear order become dynamically unstable when black holes lose the local thermodynamic stability. We discuss how dynamical instabilities can be explained by the Second Law of Thermodynamics.
We study dynamical surface gravity in a general spherically symmetric setting using Painlevé-Gullstrand (PG) coordinates. Our analysis includes several definitions that have been proposed in the past as well as two new definitions adapted to PG coordinates. Various properties are considered, including general covariance, value at extremality, locality and static limit. We illustrate with specific examples of "dirty" black holes that even for spacetimes possessing a global timelike Killing vector, local definitions of surface gravity can differ substantially from "non-local" ones that require a…
We study separatively the quasinormal modes (QNM) of electromagnetic perturbations around three-dimensional anti-de Sitter(AdS) black holes in Jordan and Einstein frames, which are related by the conformal transformations and a redefinition of a scalar field. We find that, in the Jordan frame, the imaginary parts of QNM frequencies can reflect the thermodynamical stabilities of hairy black holes, including the possible phase transition between the hairy black hole and BTZ black hole, disclosed by examining the corresponding free energies. Similar results are also uncovered in the Einstein fram…
We study conserved charges and thermodynamics of analytic rotating anti-de Sitter black holes with extended horizon topology -- also known as black strings -- in dynamical Chern-Simons modified gravity. The solution is supported by a scalar field with an axionic profile that depends linearly on the coordinate that spans the string. We compute conserved charges by making use of the renormalized boundary stress-energy tensor. Then, by adopting the Noether-Wald formalism, we compute the black string entropy and obtain its area law. Indeed, the reduced Euclidean Hamiltonian approach shows that the…
We perform the stability analysis of the Schwarzschild black hole in $f(R)$ gravity with the parity-violating Chern-Simons (CS) term coupled to a dynamical scalar field $θ$. For this purpose, we transform the $f(R)$ gravity into the scalar-tensor theory by introducing a scalaron $ϕ$, providing the dynamical Chern-Simons modified gravity with two scalars. The perturbation equation for the scalar $θ$ is coupled to the odd-parity metric perturbation equation, providing a system of two coupled second order equations, while the scalaron is coupled to the even-parity perturbation equation. This impl…
In the framework of Metric-Affine Gravity, the existing correspondence between the Einstein tensor and the energy-momentum tensor of matter provided by General Relativity is extended towards a post-Riemannian description in terms of the torsion and nonmetricity fields, which are sourced by the spin, dilation and shear currents of matter. In this work, we focus on the dynamical role of the traceless part of the nonmetricity tensor and its intrinsic connection with shears, defining a model which encloses a new black hole solution endowed with shear charges. We show that the extension in the pres…
We find black hole solutions to Euclidean 2+1 gravity coupled to a relativistic particle which have a dynamical conical singularity at the horizon. These solutions mimic the tree level contribution to the partition function of gravity coupled to a quantum field theory. They are found to violate the standard area law for black hole entropy, their entropy being proportional to the total opening angle. Since each solution depends on the number of windings of the particle path around the horizon, the significance of their summation in the path integral is considered.
In this work we derive simple closed-form expressions for the dynamical friction acting on black holes moving through ultralight (scalar field) dark matter, covering both non-relativistic and relativistic black hole speeds. Our derivation is based on long known scattering amplitudes in black hole spacetimes, it includes the effect of black hole spin and can be easily extended to vector and tensor light fields. Our results cover and complement recent numerical and previous non-relativistic treatments of dynamical friction in ultralight dark matter.
We drop the complexification procedure from the Newman-Janis algorithm and introduce more physical arguments and symmetry properties, and we show how one can generate regular and singular rotating black hole and non-black-hole solutions in Boyer-Lindquist coordinates. We focus on generic rotating regular black holes and show that they are regular on the Kerr-like ring but physical entities are undefined there. We show that rotating regular black holes have much smaller electric charges, and, with increasing charge, they turn into regular non-black-hole solutions well before their Kerr-Newman c…
We present several classes of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant. The spacetime has spherical, plane, or hyperbolic symmetry and the higher-dimensional solutions are obtained in a closed form only in the plane symmetric case. Among them, the class-I solution represents an asymptotically locally anti-de Sitter (AdS) dynamical black hole or wormhole. In four and higher dimensions, the generalized Misner-Sharp quasi-local mass blows up at AdS infinity, inferring that the spacetime is only locally AdS. In three dimensions, the scalar field becomes triv…
We consider black hole in Einstein-Gauss-Bonnet(EGB) gravity in a dynamical setup and also the stationary black hole in recently discovered\cite{Glavan} $4$-dimensional novel Einstein-Gauss-Bonnet gravity. For dynamical EGB black hole in completely local settings we calculate the temperature associated with the horizon. For the stationary black hole in $4$-dimensional novel EGB theory we explore the thermodynamic properties including calculation of temperature and entropy.
The Newman-Janis (NJ) method is a prescription to derive the Kerr space-time from the Schwarzschild metric. The BTZ, Kerr and five-dimensional Myers-Perry (MP) black hole solutions have already been generated by different versions of the NJ method. However, it is not known how to generate the metric of higher-dimensional (d > 6) rotating black holes by this method. In this paper, we propose the simplest algorithm for generation of the five-dimensional MP metric with two arbitrary angular momenta by using the Kerr-Schild form of the metric and quaternions. Then, we present another new two-step …
The generalized second law of thermodynamics for a system containing a black hole dynamical horizon is proposed in a covariant way. Its validity is also tested in case of adiabatically collapsing thick light shells.
Introducing the concept of the extreme trapping horizon, we discuss geometric features of dynamical extreme black holes in four dimensions and then derive the integral identities which hold for the dynamical extreme black holes. We address the causal/geometrical features too.
In recent times there is a surge of interest in constructing Einstein-Gauss-Bonnet (EGB) gravity, in the limit $D \to 4 $, of the $D$-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed $D \to 4 $ regularized EGB gravities coincide, and incidentally some other theories also admit the same solution. We prove a theorem that characterizes a large family of nonstatic or radiating spherically symmetric solutions to the $4D$ EGB gravity, representing, in general, spherically symmetric Type II fluid. An extension of the theorem, given without pro…
As a simple but important example of dynamical black hole, we analysis the dynamical black hole in $n$-dimensional Vaidya spacetime in detail. We investigated the thermodynamics of field equation in $n$-dimensional Vaidya spacetime. The unified first law was derived in terms of the methods proposed by Sean A Hayward. The first law of dynamical black hole was obtained by projecting the unified first law along the trapping horizon. At last, the second law of dynamical black hole is also discussed.
