We present a generalization of the Hawking effect for dynamical trapping horizons by calculating the tunneling rate in the Hamilton-Jacobi formalism. It turns out that all horizons classified by Hayward are subjected to thermal quantum effects. While the Hawking effect for future outer and past inner trapping horizons is given as a particle emission, we show that the Hawking effect for future inner and past outer trapping horizons translates to an absorption. The universality of the treatment allows a natural transfer to the static case.
A condition is defined which determines if a supertranslation is induced in the course of a general evolution from one isolated horizon phase to another via a dynamical horizon. This condition fixes preferred slices on an isolated horizon and is preserved along an Isolated Horizon. If it is not preserved, in the course of a general evolution, then a supertranslation will be said to have been induced. A simple example of spherically symmetric dynamical horizons is studied to illustrate the conditions for inducing supertranslations.
In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.
A detailed description of how black holes grow in full, non-linear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. Change in the horizon area is related to these fluxes. A notion of angular momentum and energy is associated with cross-sections of the horizon and balance equations, analogous to those obtained by Bondi and Sachs at null infinity, are derived. These in turn lead to general…
We show that the number of supersymmetries of IIB black hole horizons is N=2 N_- + 2 index(D_λ), where index(D_λ) is the index of the Dirac operator twisted with the line bundle λ^{1/2} of IIB scalars, and N_- is the dimension of the kernel of a horizon Dirac operator which depends on IIB fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries. In addition if the horizons have non-trivial fluxes and N_- is nonzero, then index(D_λ) is non-negative, and the horizons admit an sl(2,R) symmetry subalgebra. This provides evidence that all such horizons have an AdS/CFT dual. Fu…
We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are explicitly calculated to second order. For the spacelike case, knowledge of the intrinsic and extrinsic geometry of the (dynamical) horizon is sufficient to determine the near-horizon spacetime, while for the null case (an isolated horizon) more information is needed. In both cases spacetime is allowed to be of arbitrary dimension and the formalism accomodates bo…
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.
The instability against emission of fermionic particles by the trapping horizon of an evolving black hole is analyzed using the Hamilton-Jacobi tunneling method. This method automatically selects one special expression for the surface gravity of a changing horizon. The results also apply to point masses embedded in an expanding universe. As a bonus of the tunneling method, we gain the insight that the surface gravity still defines a temperature parameter as long as the evolution is sufficiently slow that the black hole pass through a sequence of quasi-equilibrium states, and that black holes s…
We here propose a covariant entropy conjecture on cosmological dynamical horizon. After the formulation of our conjecture, we test its validity in adiabatically expanding universes with open, flat and closed spatial geometry, where our conjecture can also be viewed as a cosmological version of the generalized second law of thermodynamics in some sense.
Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using…
We consider how the mass of the black hole decreases by the Hawking radiation in the Vaidya spacetime, using the concept of dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that final state is the Minkowski spacetime in our particular model.
Instead of using a three dimensional analysis on quasi-local horizons, we adopt a four dimensional asymptotic expansion analysis to study the next order contributions from the nonlinearity of general relativity. From the similarity between null infinity and horizons, the proper reference frames are chosen from the compatible constant spinors for an observer to measure the energy-momentum and flux near quasi-local horizons. In particular, we focus on the similarity of Bondi-Sachs gravitational radiation for the quasi-local horizons and compare our results to Ashtekar-Kirshnan flux formular. The…
Dynamical, non-asymptotically flat black holes are best characterized by their apparent horizons. Cosmological black hole solutions of General Relativity exhibit two types of apparent horizon behaviours which, thus far, appeared to be completely disconnected. By taking the limit to General Relativity of a class of Brans-Dicke spacetimes, it is shown how one of these two behaviours is really a limit of the other.
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master equation, which leads to a systematic construction of all spherically symmetric dynamical horizons (SSDH) satisfying certain boundedness conditions. We also find necessary and sufficient conditions for a given spherically symmetric spacetime to contain a SSDH.
We analyse the global structure of time-dependent geometries dual to expanding plasmas, considering two examples: the boost invariant Bjorken flow, and the conformal soliton flow. While the geometry dual to the Bjorken flow is constructed in a perturbation expansion at late proper time, the conformal soliton flow has an exact dual (which corresponds to a Poincare patch of Schwarzschild-AdS). In particular, we discuss the position and area of event and apparent horizons in the two geometries. The conformal soliton geometry offers a sharp distinction between event and apparent horizon; whereas t…
A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract physicaly relevant quantities describing the horizon irrespective to whether it is isolated (null) or dynamical at a given instant of time. Furthermore, small perturbation of isolated horizons are considered, and finally a family of axially--symmetric exact solution of the constraint equations on a dynamical horizon is presented.
The entropy bound conjecture concerning black hole dynamical horizons is proved. The conjecture states, if a dynamical horizon, $D_H$, is bounded by two surfaces with areas of $A_B$ and $\abp$ ($\abp>A_B$), then the entropy, $S_D$, that crosses $D_H$ must satisfy $S_D\leq {1/4}(\abp-A_B)$. We show that this conjecture is implied by the generalized Bousso bound. Consequently, the generalized second law holds for dynamical horizons. Finally, we show that the lightlike bousso bound and its spacelike counterpart can be unified as one bound.
We propose a special solution of Einstein equations in the general Vaidya form representing a dynamical black hole having horizon cross-sections with toroidal topology. The concrete model enables us to study for the first time dynamical horizons with toroidal topology, its area law, and the question of matter flux inside the horizon, without using a cut-and-paste technology to construct the solution.
In arXiv:1310.3727 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed by the linearized equations of motion and symmetry conditions which we carefully specify, satisfy the EPL. We also show that these perturbations are limited to those coming from difference o…
Recently, we have generalized the Bekenstein-Hawking entropy formula for black holes embedded in expanding Friedmann universes. In this letter, we begin the study of this new formula to obtain the first law of thermodynamics for dynamical apparent horizons. In this regard we obtain a generalized expression for the internal energy $U$ together with a distinction between the dynamical temperature $T_D$ of apparent horizons and the related one due to thermodynamics formulas. Remarkable, when the expression for $U$ is applied to the apparent horizon of the universe, we found that this internal ene…
We examine the evolution of extremal spherically symmetric black holes, developing both general theory as well as the specific cases of (charged) null dust and massless scalar field spacetimes. As matter accretes onto extremal marginally trapped tubes, they generically evolve to become non-extremal with the initial extremal horizon bifurcating into inner and outer non-extremal horizons. At the start of this process arbitrarily slow matter accretion can cause a geometrically invariant measure of horizon growth to jump from zero to infinity. We also consider dynamical horizons that are extremal …
Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form…
In the paper, the temperature associated with a dynamical spherically symmetric black hole or with a cosmological horizon is investigated from the point of view of a point-like detector. First, we briefly review the Hamilton-Jacobi tunneling method for a generic dynamical spherically symmetric space-time, and present two applications of the tunneling method. Then, we apply a well-known relativistic quantum theoretical technique, namely the Unruh-DeWitt detector formalism for a conformally coupled scalar field in a generic FRW space-time. As an application, for the generic static black hole cas…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theorems for dynamical horizons. Ramifications of some of these results to numerical simulations of black hole spacetimes are discussed. Finally several expectations on the interplay between isometries and dynamical horizons are shown to be borne out.
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law h…
Dynamical horizons are considered in full, non-linear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive and change in the horizon area is related to these fluxes. The flux formulae also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide generalizations of the first and second laws of black hole mechanics.
Using the recent thermodynamical study of isolated horizons by Ghosh and Perez, we provide a statistical mechanical analysis of isolated horizons near equilibrium in the grand canonical ensemble. By matching the description of the dynamical phase in terms of weakly dynamical horizons with this local statistical framework, we introduce a notion of temperature in terms of the local surface gravity. This provides further support to the recovering of the semiclassical area law just by means of thermodynamical considerations. Moreover, it allows us to study the radiation process generated by the LQ…
In this paper, we investigate the dynamical formation and evolution of 2 + 1-dimensional charged black holes. We numerically study dynamical collapses of charged matter fields in an anti de Sitter background and note the formation of black holes using the double-null formalism. Moreover, we include re-normalized energy-momentum tensors assuming the S-wave approximation to determine thermodynamical back-reactions to the internal structures. If there is no semi-classical effects, the amount of charge determines the causal structures. If the charge is sufficiently small, the causal structure has …
We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. This discrete quantum hair structure associated to the horizon geometry produc…
Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and a Killing horizon of the static spacetime. We show how this conformal relation can be used to derive thermodynamic properties for the dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetim…
A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a parameter e which characterizes how close a horizon is to extremality and should be calculable in numerical simulations.
We examine the nonlinear classical dynamics of a fundamental string in anti-de Sitter spacetime. The string is dual to the flux tube between an external quark-antiquark pair in $\mathcal{N}=4$ super Yang-Mills theory. We perturb the string by shaking the endpoints and compute its time evolution numerically. We find that with sufficiently strong perturbations the string continues extending and plunges into the Poincaré horizon. In the evolution, effective horizons are also dynamically created on the string worldsheet. The quark and antiquark are thus causally disconnected, and the string transi…
We address the question whether or not two electrically charged elementary particles can Coulomb scatter if one of these particles is inside the Schwarzschild black-hole horizon and the other outside. It can be shown that the quantum process is consistent with the local energy-momentum conservation law. This result implies that across-horizon scattering is a physical effect, relevant to astrophysical black holes. We propose a Gedankenexperiment which uses the quantum scattering process to transfer information from inside the black-hole horizon to outside.
Causal horizons in pure Poincare $AdS$ are Killing horizons generated by dilatation vector. Renormalization group (RG) flow breaks the dilatation symmetry and makes the horizons dynamical. We propose that the boundary RG flow is dual to the thermodynamics of the causal horizon. As a check of our proposal we show that the gravity dual of the boundary $c$-theorem is the second law of thermodynamics obeyed by causal horizons. The holographic $c$-function is the Bekenstein-Hawking entropy (density) of the dynamical causal horizon. We explicitly construct the $c$-function in a generic class of RG-f…
In this work, we uncover new features in the evolution of the deformations of the dynamical horizon geometry in a binary black hole merger scenario using numerical relativity. First, in the inspiral phase, owing to the deformations, the dynamical horizons of the two black holes are found to steadily acquire multipole moments that vanish when the horizons are isolated. Out of these, the dominant moment is found to be the quadrupole moment. Second, we show that they encode detailed information about the dynamics of the binary black hole system. The dominant quadrupole multipole moment is particu…
An insightful viewpoint was proposed by Susskind about AMPS firewall: the region behind the firewall does not exist and the firewall is an extension of the singularity. In this work, we provided a possible picture of this idea by combining Newman's complex metric and Dvali-Gomez BEC black holes, which are Bose-Einstein condensates of N gravitons. The inner space behind the horizon is a realized imaginary space encrusted by the real space outside the horizon. In this way, the singularity extents to the horizon to make a firewall for the infalling observer. Some gravitons escape during the fluct…
The extended holographic dark energy model with the Hubble horizon as the infrared cutoff avoids the problem of the circular reasoning of the holographic dark energy model. Unfortunately, it is hit with the no-go theorem. In this paper, we consider the extended holographic dark energy model with a potential, $V(ϕ)$, for the Brans-Dicke scalar field. With the addition of a potential for the Brans-Dicke scalar field, the extended holographic dark energy model using the Hubble horizon as the infrared cutoff is a viable dark energy model, and the model has the dark energy dominated attractor solut…
Our knowledge of dynamical black holes suffers from a lack of observational insight. In an analogue model of gravity, we can design a longitudinally symmetric dynamical acoustic black hole with a moving horizon. In this symmetric spacetime, the marginally outer trapped surface and the so called evolving horizon are degenerate. Interestingly, there are many ways of assigning a surface gravity to the horizon in the absence of time translation invariance. Here, we present two of them that are distinguished by whether they are defined only locally or take into account the global properties of spac…
We investigate some of the issues relating to the dynamical instability of general static spacetimes with horizons. Our paper will be partially pedagogical and partially exploratory in nature. After discussing the current understanding, we generalize the proposal of Gubser and Mitra, which identifies dynamical instability of black branes with local thermodynamic instability, to include all product spacetimes with the horizon uniformly smeared over an internal space. We support our conjecture by explicitly exhibiting a threshold unstable mode for Schwarzschild-AdS_5 x S^5 black hole. Using the …
We prove that Killing horizons in massive IIA supergravity preserve an even number of supersymmetries, and that their symmetry algebra contains an $\mathfrak{sl}(2, R)$ subalgebra, confirming the conjecture of [5]. We also prove a new class of Lichnerowicz type theorems for connections of the spin bundle whose holonomy is contained in a general linear group.
As a compelling pattern for the holographic principle, our covariant entropy bound conjecture is proposed for more general dynamical horizons. Then we apply our conjecture to $Λ$CDM cosmological models, where we find it imposes a novel upper bound $10^{-90}$ on the cosmological constant for our own universe by taking into account the dominant entropy contribution from super-massive black holes, which thus provides an alternative macroscopic perspective to understand the longstanding cosmological constant problem. As an intriguing implication of this conjecture, we also discuss the possible pro…
The paper deals with anisotropic spherically symmetric Lemaitre-Tolman-Bondi model of the universe bounded by the apparent horizon. Using Hamilton-Jacobi method for both massive and massless test particles, we are able to show that the temperature associated with the apparent horizon due to Hawking radiation is the usual Hawking Temperature. Also the usual Lemaitre-Tolman-Bondi model and the transformed r-gauge Lemaitre-Tolman-Bondi model are shown to be equivalent. Finally, the results of Tunneling approach agree with the Hamiltonian-Jacobi method.
Physical process version of the first law of black hole mechanics relates the change in entropy of a perturbed Killing horizon, between two asymptotic cross sections, to the matter flow into the horizon. Here, we study the mathematical structure of the physical process first law for a general diffeomorphism invariant theory of gravity. We analyze the effect of ambiguities in the Wald's definition of entropy on the physical process first law. We show that for linearized perturbations, the integrated version of the physical process law, which determines the change of entropy between two asymptot…
Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or spacelike everywhere. Furthermore, we discuss the relation between ``bounding'' and ``stability'' properties of marginally outer trapped surfaces.
We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This reflects the local character of trapping horizons as opposed to event horizons. Interpreting the area as the entropy, w…
