Modifying the Kerr-Schild transformation used to generate black and white hole spacetimes, new dynamic black and white holes are obtained using a time-dependent Kerr-Schild scalar field. Physical solutions are found for black holes that shrink with time and for white holes that expand with time. The black hole spacetimes are physical only in the vicinity of the black hole, with the physical region increasing in radius with time. The white hole spacetimes are physical throughout. Unlike the standard Schwarzschild solution the singularities are non-isolated, since the time-dependence introduces a mass-energy distribution. The surfaces in the metrics where g_{tt}=g^{rr}=0 are dynamic, moving inward with time for the black holes and outward for the white holes, which leads to a question of whether these spacetimes truly have event horizons--a problem shared with Vaidya's cosmological black hole spacetimes. By finding a surface that shrinks or expands at the same rate as the null geodesics move, and within which null geodesics move inward or outward faster than the surfaces shrink or expand respectively, it is verified that these do in fact behave like black and white holes.
We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.
Quantum tunneling of a black hole into a white hole provides a model for the full life cycle of a black hole. The white hole acts as a long-lived remnant, solving the black-hole information paradox. The remnant solution of the paradox has long been viewed with suspicion, mostly because remnants seemed to be such exotic objects. We point out that (i) established physics includes objects with precisely the required properties for remnants: white holes with small masses but large finite interiors; (ii) non-perturbative quantum-gravity indicates that a black hole tunnels precisely into such a whit…
This paper considers a wider range of "quasi-classical" models for the non-singular transition from an evaporating black hole to a white hole and the evolution of the white hole than were considered in Paper I. The quantum evolution of the geometry outside a collapsing shell is described by a smoothly evolving spherically symmetric effective metric, with a transition from trapped surfaces in the black hole to anti-trapped surfaces in the white hole at a spacelike hypersurface on which the circumferential radius has a minimum Planck-scale value. Rather than focusing on a specific model for the …
The comment arXiv:1204.2729v1 is completely wrong. The author makes serious mistakes in calculations and judgement. The errors are made at the level of basic undergraduate statistical mechanics.
We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with the horizon as an inner boundary. The spacetime metric and other geometric fields are expanded in a power series in a radial coordinate away from the horizon by solving the characteristic field equations in the Newman-Penrose formalism. This is the first in a series of papers which investigate the near horizon geometry and its physical applications using the …
A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A space-time representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon . Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced. Although these definitions do not refer to infinity, the quantities assume their standard values in Reissner-Nordstrom solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolate…
We study static, spherically symmetric, Skyrme black holes in the context of the assumption that they can be viewed as bound states between ordinary bare black holes and solitons. This assumption and results stemming from the isolated horizons formalism lead to several conjectures about the static black hole solutions. These conjectures are tested against the Skyrme black hole solutions. It is shown that, while there is in general good agreement with the conjectures, a crucial aspect seems to violate one of the conjectures.
It is shown that a black hole can be in two states: one with positive and other with negative surface gravity $k$. The state with $k<0$ corresponds to a white hole. In this state there is no information loss. In the quantization of black hole area the surface of a black hole is divided into a system of independent patches, each of which can be in two states: one with $k>0$ and other with $k<0$. Then the entropy goes like the area and information can be recovered from the black hole.
We investigate particle collisions in non-extremal black hole that can probably induced to extremely high center of mass energy $E_{\text{cm}}$. We consider the collision of two particles where first particle comes from far to the outer horizon of the Reissner-Nordström black hole and second particle emanates from the white hole region. It is exhibited that unbounded $E_{\text{cm}}$ requires that second particle lapse near the bifurcation point. We discuss the collision of particles close to the outer horizon in detail.
In this paper, by setting proper boundaries in the Minkowski spacetime, we construct three toy model spacetimes, a toy black hole, a toy white hole, and a toy wormhole. Based on these model spacetimes, we discuss the Hawking radiation and the information loss problem. By counting the number of the field modes inside and outside the horizon, we show the thermal radiation of the toy black hole. We show that the white hole have a thermal absorption. We show that in the whole toy wormhole spacetime, there is no information lost. In addition, we show the black hole radiation and the white hole abso…
Boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon. Inspired by Hamiltonian mechanics, a (quasi-)local definition of isolated horizon mass is formulated. Although its definition does not refer to infinity, this mass takes the standard value in a Reissner-Nordstrom solution. Furthermore, under certain technical assumptions, the mass of an isolated horizon is shown to equal the future limit of the Bondi energy.
Isolated horizon conditions enforce the time invariance of both the intrinsic and the extrinsic geometry of a (quasilocal) black hole horizon. Nonexpanding horizons, only requiring the invariance of the intrinsic geometry, have been successfully employed in the (excision) initial data of black holes in instantaneous equilibrium. Here we propose the use of the full isolated horizon structure when solving the elliptic system resulting from the complete set of conformal 3+1 Einstein equations under a quasiequilibrium ansatz prescription. We argue that a set of geometric inner boundary conditions …
We give a short introduction to the approaches currently used to describe black holes in loop quantum gravity. We will concentrate on the classical issues related to the modeling of black holes as isolated horizons, give a short discussion of their canonical quantization by using loop quantum gravity techniques, and a description of the combinatorial methods necessary to solve the counting problems involved in the computation of the entropy.
Recent detailed analysis within the Loop Quantum Gravity calculation of black hole entropy shows a stair-like structure in the behavior of entropy as a function of horizon area. The non-trivial distribution of the degeneracy of the black hole horizon area eigenstates is at the origin of this behavior. This degeneracy distribution is analyzed and a phenomenological model is put forward to study the implications of this distribution in the black hole radiation spectrum. Some qualitative quantum effects are obtained within the isolated horizon framework. This result provides us with a possible ob…
Black holes formation and evolution have been extensively studied at the classical level. However, not much is known regarding the end of their lives, a phase that requires to consider the quantum nature of the gravitational field. A black-to-white hole transition can capture the physics of this phenomenon, in particular the physics of the residual small black holes at the end of the Hawking evaporation. This work shows how the spin foam formalism is able to describe this non-perturbative phenomenon. A thorough examination of the black hole spacetime region in which quantum effects cannot be n…
We investigate isolated white holes surrounded by vacuum, which correspond to the time reversal of eternal black holes that do not evaporate. We show that isolated white holes produce quasi- thermal Hawking radiation. The time reversal of this radiation, incident on a black hole precursor, constitutes a special preparation that will cause the black hole to become eternal.
Using the canonical quantum theory of spherically symmetric pure gravitational systems, we present a direct correspondence between the Friedmann-Robertson-Walker (FRW) cosmological model in the interior of a Schwarzschild black hole and the nth energy eigenstate of a linear harmonic oscillator. Such type of universe has a quantized mass of the order of the Planck mass and harmonic oscillator wave functions
The near horizon geometry of general black holes in equilibrium can be conveniently characterized in the formalism of weakly isolated horizons in the form of the Bondi-like expansions (Krishnan B, Class.\ Quantum Grav.\ 29, 205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has been extensively investigated in the weakly isolated horizon framework, the off-horizon description in the Bondi-like system employed by Krishnan has not been studied. We extend Krishnan's work by explicit, non-perturbative construction of the Bondi-like tetrad in the full Kerr-Newman spacetime. N…
We write explicitly the complete Lorentzian metric of a singularity-free spacetime where a black hole transitions into a white hole located in its same asymptotic region. In particular, the metric interpolates between the black and white horizons. The metric satisfies the Einstein field equations up to the tunneling region. The matter giving rise to the black hole is described by the Oppenheimer-Snyder model, corrected with loop-quantum-cosmology techniques in the quantum region. The interior quantum geometry is fixed by a local Killing symmetry, broken at the horizon transition. At large scal…
A self-consistent exact solution for a Reissner-Nordström black-and-white hole formed as a result of accretion has been considered. Prior to the formation of a black-and-white hole, there is a bulk charged sphere at the center of the system. The occurrence of a turning (bounce) point in the newly formed black-and-white hole is investigated. The occurrence of a turning point was investigated by an example of solution for the accretion of a neutral spherical dust shell. The model equations are written with allowance for the cosmological $Λ$-term. Within the model under consideration, both the bl…
This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the cla…
Recently a consistent non-perturbative quantization of the Schwarzschild interior resulting in a bounce from black hole to white hole geometry has been obtained by loop quantizing the Kantowski-Sachs vacuum spacetime. As in other spacetimes where the singularity is dominated by the Weyl part of the spacetime curvature, the structure of the singularity is highly anisotropic in the Kantowski-Sachs vacuum spacetime. As a result the bounce turns out to be in general asymmetric creating a large mass difference between the parent black hole and the child white hole. In this manuscript, we investigat…
We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary co…
Recently, O.B.Zaslavskii considers the collision near the horizon of the extremal Kerr black hole that produces two particles and one of two particles has divergent conserved killing energy(the so called super Penrose process). O.B.Zaslavskii shows this particle can not move in a asymptotic region in this universe. This means super Penrose process for extremal Kerr black hole is impossible. However, recently, Mandar Patil and Tomohiro Harada show this particle can enter event horizon, turns back and emerges through white hole event horizon into asymptotic region in other universe. This means s…
We present an exact solution of the Maxwell-Einstein equations, which describes the exterior of a charged spherical mass collapsing into its own trapping horizon and then bouncing back from an anti-trapping horizon at the same space location of the same asymptotic region. The solution is locally but not globally isometric to the maximally extended Reissner-Nordström metric and depends on seven parameters. It is regular, and defined everywhere except for a small region, where quantum tunnelling is expected. This region lies outside the mass: the mass-bounce and its near exterior are governed by…
The Isolated Horizons (IH) formalism, together with a simple phenomenological model for colored black holes has been used to predict non-trivial formulae that relate the ADM mass of the solitons and hairy Black Holes of Gravity-Matter system on the one hand, and several horizon properties of the black holes in the other. In this article, the IH formalism is tested numerically for spherically symmetric solutions to an Einstein-Higgs system where hairy black holes were recently found to exist. It is shown that the mass formulae still hold and that, by appropriately extending the current model, o…
There is a deep underlying problem in the model dependent thermodynamic analysis of black holes shown in the above quoted paper. In this method one can only find out the canonical entropy of the black hole but not the `microcanonical' entropy. Besides this crucial issue a few other problems are also discussed.
We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the Conformal Thin Sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the Isolated Horizons formalism. We then investigate the application of these conditions to the Initial Data Problem of binary black holes and discuss the relation of our…
Black hole mechanics was recently extended by replacing the more commonly used event horizons in stationary space-times with isolated horizons in more general space-times (which may admit radiation arbitrarily close to black holes). However, so far the detailed analysis has been restricted to non-rotating black holes (although it incorporated arbitrary distortion, as well as electromagnetic, Yang-Mills and dilatonic charges). We now fill this gap by first introducing the notion of isolated horizon angular momentum and then extending the first law to the rotating case.
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them ({\it unconstrained} evolution). The problem of the 3-d computational simulation of even a single isolated vacuum black hole has proven to be remarkably difficult. Recently, we have become aware of two publications that describe very long term evolution, at least …
A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A space-time representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such a horizon. However, the definition is applicable in a more general context, such as cosmological horizons. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced and their properties analyzed. Although their definitions do not refer to infinity, these quantities assume their standard values in t…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the existence of a particle, which is an event. In the commonly accepted approach, singularities are not incorporated into spacetime. Thus spacetime turns out to be event-incomplete. With creation from nothing, singularities are sources of lawlessness. A straightforward way around those conceptual problems consists in including metric singularities in spacetime and then…
Black holes are important astrophysical objects describing an end state of stellar evolution, which are observed frequently. There are theoretical predictions that Kerr black holes with high spins expel magnetic fields. However, Kerr black holes are pure vacuum solutions, which do not include accretion disks, and additionally previous investigations are mainly limited to weak magnetic fields. We prove for the first time in full general relativity that generic rapidly spinning black holes including those deformed by accretion disks still expel even strong magnetic fields. Analogously to a simil…
We show that the expected lifetime of white holes formed as remnants of evaporated black holes is consistent with their production at reheating. We give a simple quantum description of these objects and argue that a quantum superposition of black and white holes with large interiors is stable, because it is protected by the existence of a minimal eigenvalue of the area, predicted by Loop Quantum Gravity. These two results support the hypothesis that a component of dark matter could be formed by small black hole remnants.
Hawking radiation is nowadays being understood as tunnelling through black hole horizons. Here, the extension of the Hamilton-Jacobi approach to tunnelling for non-rotating and rotating black holes in different non-singular coordinate systems not only confirms this quantum emission from black holes but also reveals the new phenomenon of absorption into white holes by quantum mechanical tunnelling. The role of a boundary condition of total absorption or emission is also clarified.
This is the first of two papers presenting different versions of quasi-classical toy models for the non-singular evolution of the geometry and the associated effective stress-energy tensor for a spherically symmetric black hole that evolves into a white hole and eventually disappears after evaporating down to the Planck scale. The ansatz for the geometry is inspired by calculations of the semi-classical stress-energy tensor in the Schwarzschild background and ideas from loop quantum gravity for a nonsingular transition to the white hole. In this paper the main emphasis is on the evolution of t…
Recently, various authors have proposed that the first ultraviolet effect on the gravitational collapse of massive stars to black holes is the transition between a black-hole geometry and a white-hole geometry, though their proposals are radically different in terms of their physical interpretation and characteristic time scales [1,2]. Several decades ago, it was shown by Eardley that white holes are highly unstable to the accretion of small amounts of matter, being rapidly turned into black holes [3]. Studying the crossing of null shells on geometries describing the black-hole to white-hole t…
The possibility that a black hole could tunnel into a white hole has recently received attention. Here we present a metric that improves the 'firework' metric: it describes the entire process and solves the Einstein equations everywhere except on a small transition surface that corresponds to the quantum tunnelling. We compute the corresponding ray-tracing map from past infinity to future infinity explicitly.
This is a concise review, addressed to undergraduate students, of S. Chandrasekhar's oeuvre in astrophysics, ranging from his early studies on white dwarfs using relativistic quantum statistics to topics as diverse as dynamical friction, negative hydrogen ion, fluid dynamical instabilities, black holes and gravitational waves. The exposition is based on simple physical explanations in the context of observational astronomy. Black holes and their role as central engines of active, compact, high energy sources have been discussed.
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreem…
By utilizing the thin shell approximation, we investigate the behavior of radial timelike geodesics in a black hole to white hole bouncing scenario with a mass (de-)amplification relation. We show that those geodesics lose energy after crossing the transition surface if the white hole mass is less than the black hole mass and vice versa. That is, the bounded timelike radial geodesics become closer to the event horizon in the mass decreasing direction. We then show that by tracing a finite amount of bouncing cycles along the mass decreasing direction, all bounded radial geodesics can be squeeze…
A finite-length magnetic vortex line solution is derived within the context of (4-dim) dilaton gravity. We approach the Bonnor metric at the Einstein-Maxwell limit, and encounter the "flux tube as (Euclidean) Kerr horizon" at the Kaluza-Klein level. Exclusively for string theory, the magnetic flux tube world-sheet exhibits a 2-dim black & white dihole structure. (The figure has been cut off, and is now available upon request from davidson@bguvms.bgu.ac.il)
White dwarfs inspiraling into black holes of mass $\MBH\simgt 10^5M_\odot$ are detectable sources of gravitational waves in the LISA band. In many of these events, the white dwarf begins to lose mass during the main observational phase of the inspiral. The mass loss starts gently and can last for thousands of orbits. The white dwarf matter overflows the Roche lobe through the $L_1$ point at each pericenter passage and the mass loss repeats periodically. The process occurs very close to the black hole and the released gas can accrete, creating a bright source of radiation with luminosity close …
We show that there is a classical metric satisfying the Einstein equations outside a finite spacetime region where matter collapses into a black hole and then emerges from a white hole. We compute this metric explicitly. We show how quantum theory determines the (long) time for the process to happen. A black hole can thus quantum-tunnel into a white hole. For this to happen, quantum gravity should affect the metric also in a small region outside the horizon: we show that contrary to what is commonly assumed, this is not forbidden by causality or by the semiclassical approximation, because quan…
The spacetime inside the white hole is like an anisotropic cosmological background with the past singularity playing the role of a big bang singularity. The scale factor along the extended spatial direction is contracting while the scale factor along the two-sphere is expanding. We consider an eternal Schwarzschild manifold and study quantum cosmological perturbations generated near the white hole singularity which propagate towards the past event horizon and to exterior of the black hole. It is shown that an observer deep inside the white hole and an observer far outside the black hole both s…
We present calculations indicating the possibility of a new class of Type I supernovae. In this new paradigm relativistic terms enhance the self gravity of a carbon-oxygen white dwarf as it passes or orbits near a black hole. This relativistic compression can cause the central density to exceed the threshold for pycnonuclear reactions so that athermonuclear runaway ensues. We consider three possible environments: 1) white dwarfs orbiting a low-mass black hole; 2) white dwarfs encountering a massive black hole in a dense globular cluster; and 3) white dwarfs passing a supermassive black hole in…
Electrons in Type II Weyl semimetals display one-way propagation, which supports totally reflecting behavior at an endpoint, as one has for black hole horizons viewed from the inside. Junctions of Type I and Type II lead to equations identical to what one has near black hole horizons, but the physical implications, we suggest, are quite different from expectations which are conventional in that context. The time-reversed, "white hole" configuration is also physically accessible.
A new scenario for gravitational collapse has been recently proposed by Haggard and Rovelli. Presenting the model under the name of black hole fireworks, they claim that the accumulation of quantum gravitational effects outside the horizon can cause the tunneling of geometry from a black hole to a white hole, allowing a bounce of the collapsing star which can eventually go back to infinity. In this paper we discuss the instabilities of this model and propose a simple minimal modification which eliminates them, as well as other related instabilities discussed in the literature. The new scenario…
