We prove that the black to white hole transition theorized in several papers can be described as a change in the topology of the event horizon. We also show, using the theory of cobordism due to Milnor and Wallace, how to obtain the full manifold containing the transition.
The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizons. Moreover, these aspects can be removed by an appropriate timeslicing. The result will be useful to …
The crease set of an event horizon is studied in a spacetime with discrete or continuous symmetry. It determines possible topologies on spatial sections of an event horizon. We thereby investigate the classification of stable topological structure of the crease sets in a spacetime with any symmetry. In practice, we show the classification of the crease set in axially symmetric spacetime. By that we realize the topological structure of axially symmetric event horizons. We will finc that many new topological structures become stable which is not stable without symmetry.
Despite of over thirty years of research of the black hole thermodynamics our understanding of the possible role played by the inner horizons of Reissner-Nordström and Kerr-Newman black holes in black hole thermodynamics is still somewhat incomplete: There are derivations which imply that the temperature of the inner horizon is negative and it is not quite clear what this means. Motivated by this problem we perform a detailed analysis of the radiation emitted by the inner horizon of the Reissner-Nordström black hole. As a result we find that in a maximally extended Reissner-Nordström spacetime…
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.
The topology of the event horizon (TOEH) is usually believed to be a sphere. Nevertheless, some numerical simulations of gravitational collapse with a toroidal event horizon or the collision of event horizons are reported. Considering the indifferentiability of the event horizon (EH), we see that such non-trivial TOEHs are caused by the set of endpoints (the crease set) of the EH. The two-dimensional (one-dimensional) crease set is related to the toroidal EH (the coalescence of the EH). Furthermore, examining the stability of the structure of the endpoints, it becomes clear that the spherical …
We perform numerical simulations of gravitational collapse in Einstein-aether theory. We find that under certain conditions, the collapse results in the temporary formation of a white hole horizon.
We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from t…
We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks-Girardeau gas) we show that, by switching on a step potential, either a sonic (black-hole-like) horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated w…
All supersymmetric N=1, D=4 supergravity horizons have toroidal or spherical topology, irrespective of whether the black hole preserves any supersymmetry.
We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2…
We investigated the relation between the behavior of gravitational wave at late time and the limit structure of future null infinity tangent which will determine the topology of the event horizon far in the future. In the present article, we mainly consider a spacetime with two black holes. Although in most of cases, the black holes coalesce and its event horizon is topologically a single sphere far in the future, there are several possibilities that the black holes never coalesce and such exact solutions as examples. In our formulation, the tangent vector of future null infinity is, under con…
We provide experimental details of the first experiment made in zero temperature limit ($\sim$ 600\,$μ$K) studying the magnonic black/white hole horizon analogue using absolutely pure physical system based on the spin superfluidity in superfluid $^3$He-B. We show that spin precession waves propagating on the background of the spin super-currents in a channel between two Bose-Einstein condensates of magnons in form of homogeneously precessing domains mimic the properties of the black/white horizon. Once the white hole horizon is formed and blocks the propagation of the spin-precession waves bet…
Artificial black holes, such as sonic holes in Bose-Einstein condensates, may give insights into the role of the physics at the event horizon beyond the Planck scale. We show that sonic white holes give rise to a discrete spectrum of instabilities that is insensitive to the analogue of trans-Planckian physics for Bose-Einstein condensates.
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…
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…
We find the first binary black hole event horizon with a toroidal topology. It had been predicted that generically the event horizons of merging black holes should briefly have a toroidal topology, but such a phase has never been seen prior to this work. In all previous binary black hole simulations, in the coordinate slicing used to evolve the black holes, the topology of the event horizon transitions directly from two spheres during the inspiral to a single sphere as the black holes merge. We present a coordinate transformation to a foliation of spacelike hypersurfaces that "cut a hole" thro…
We study acoustic white holes in a steadily flowing atomic Bose-Einstein condensate. A white hole configuration is obtained when the flow velocity goes from a super-sonic value in the upstream region to a sub-sonic one in the downstream region. The scattering of phonon wavepackets on a white hole horizon is numerically studied in terms of the Gross-Pitaevskii equation of mean-field theory: dynamical stability of the acoustic white hole is found, as well as a signature of a nonlinear back-action of the incident phonon wavepacket onto the horizon. The correlation pattern of density fluctuations …
Hawking's topology theorem in general relativity restricts the cross-section of the event horizon of a black hole in $3+1$ dimension to be either spherical or toroidal. The toroidal case is ruled out by the topology censorship theorems. In this article, we discuss the generalization of this result to black holes in $f(R)$ gravity in $3+1$ and higher dimensions. We obtain a sufficient differential condition on the function $f'(R)$, which restricts the topology of the horizon cross-section of a black hole in $f(R)$ gravity in $3+1$ dimension to be either $S^2$ or $S^1 \times S^1$. We also extend…
We present numerical evidence for the existence of new black hole solutions in $d\geq 6$ spacetime dimensions. They approach asymptotically the Minkowski background and have an event horizon topology $S^2\times S^{d-4}$. These static solutions share the basic properties of the nonrotating black rings in five dimensions, in particular the presence of a conical singularity.
We consider a quantum analogue of black holes and white holes using Bose-Einstein condensates. The model is described by the nonlinear Schrodinger equation with a 'stream flow' potential, that induces a spatial translation to standing waves. We then mainly consider the dynamics of dark solitons in a black hole or white hole flow analogue and their interactions with the event horizon. A reduced equation describing the position of the dark solitons was obtained using variational method. Through numerical computations and comparisons with the analytical approximation we show that solitons can pas…
In this paper we find new examples of Riemannian manifolds with outermost apparent horizons with nonspherical topology, in dimensions four and above. More precisely, for any $n,m\ge1$, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology $S^n\times S^{m+1}$. In the context of general relativity these hypersurfaces correspond to outermost apparent horizons of black holes.
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…
We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. …
In four dimensions the topology of the event horizon of an asymptotically flat stationary black hole is uniquely determined to be the two-sphere $S^2$. We consider the topology of event horizons in higher dimensions. First, we reconsider Hawking's theorem and show that the integrated Ricci scalar curvature with respect to the induced metric on the event horizon is positive also in higher dimensions. Using this and Thurston's geometric types classification of three-manifolds, we find that the only possible geometric types of event horizons in five dimensions are $S^3$ and $S^2 \times S^1$. In s…
We consider a process where two identical massive particles fall inwards, starting from rest at infinity towards the extremal Kerr black hole, collide outside the event horizon in its vicinity and produce two massless particles. The center of mass energy of collision between the two particles diverges if one of the particle admits a specific critical value of the angular momentum and if the collision takes place at a location arbitrarily close to the event horizon. Assuming the isotropic emission of particles in the center of mass frame we show that one of the massless particles produced has d…
Motivated by the ideas of analogue gravity, we have performed experiments in a flume where an analogue White Hole horizon is generated, in the form of a wave blocking region, by suitably tuned uniform fluid (water) flow and counter-propagating shallow water waves. We corroborate earlier experimental observations by finding a critical wave frequency for a particular discharge above which the waves are effectively blocked beyond the horizon. An obstacle, in the form of a bottom wave, is introduced to generate a sharp blocking zone. All previous researchers used this obstacle. A novel part of our…
In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.
We argue that the formation of a Schwarzschild black hole via Datt-Oppenheimer-Snyder type gravitational collapse must be accompanied by a change in topology upon formation of the event horizon which physically separates matter in the interior from that of the exterior. While it is true that collapsing matter crossing the event horizon continues to fall towards the singularity of the Schwarzschild interior, this region does not in fact contain the matter originally responsible for the collapse. Rather, the latter occupies a distinct internal spacetime region with its own independent evolution.…
In 4-dimensional General Relativity, there are several theorems restricting the topology of the event horizon of a black hole. In the stationary case, black holes must have a spherical horizon, while a toroidal spatial topology is allowed only for a short time. In this paper, we consider spinning black holes inspired by Loop Quantum Gravity and by alternative theories of gravity. We show that the spatial topology of the event horizon of these objects changes when the spin parameter exceeds a critical value and we argue that the phenomenon may be quite common for non-Kerr black holes. Such a po…
We obtain one family of dynamic solutions in the Einstein-Maxwell-scalar(EMS) theory. Our solutions could describe the evolving charged black(white) hole or wormhole and its transition, including the case of black bounce/wormhole transition. We compare different wormhole throat definitions and suggest that the usage of trapping horizons is the most suitable choice for tracking the evolution of the dynamic black(white) hole and wormhole, and their conversion in a unified framework. Then we research several evolving processes in the appropriate parameters region, including the charge, the initia…
Using horizon shadows to distinguish a black hole and a white hole
College of Science, Northeast Forestry University（东北林业大学理学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）
We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface Sigma of constant negative or zero curvature. When horizons exist, the spacetimes are black holes with an asymptotically locally anti-de Sitter infinity, but the infinity topology differs from that in the asymptotically Minkowski case, and the horizon topology is not S^2. Maximal analytic extensions of the solutions are given. The local Hawking temperature is found. When Sigma is closed, we derive the first law of thermodynamics using a Brown-York type q…
We study the mechanics of D-dimensional isolated horizons (IHs) for Einstein gravity in the presence of arbitrary p-form matter fields. This generalizes the analysis of Copsey and Horowitz to non-stationary spacetimes and therefore the local first law to include non-monopolar (dipole) charges. The only requirement for the local first law to hold is that the action has to be differentiable. The resulting conserved charges are all intrinsic to the horizon and are independent of the topology of the horizon cross sections. We explicitly calculate the local charges for five-dimensional black holes …
The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain constraints on the nature of black hole topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of an exterior of the black hole region is always connected.…
We investigate possible geometries allowing transitions from a black hole to a white hole spacetime, by placing a space-like thin shell between them. Such proposals have been advanced recently to account for singularity-resolution in black-hole spacetimes. This space-like shell can be extended to be outside the event horizon and, thereby, reproduce some of the features of these proposals. On the other hand, if the space-like shell is confined fully within the horizon, then it results in a bounce near a space-like singularity inside the black hole. For both cases, the null energy condition is n…
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.
Although a black hole need not be spherical in higher dimensions, its event horizon cannot have arbitrary topology. Here we review some of the known constraints on horizon topology for higher dimensional black holes.
We construct static, nonextremal black hole solutions of the Einstein-Maxwell equations in $d=6,7$ spacetime dimensions, with an event horizon of $S^2\times S^{d-4}$ topology. These configurations are asymptotically flat, the U(1) field being purely magnetic, with a spherical distribution of monopole charges but no net charge measured at infinity. They can be viewed as generalizations of the $d=5$ static dipole black ring, sharing its basic properties, in particular the presence of a conical singularity. The magnetized version of these solutions is constructed by applying a Harrison transforma…
A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole would have to be sufficiently large that we can fit comfortably inside the event horizon at the present time, so that the inhomogeneities of space-time are not in contradiction with current observational limits. A specific Lemaitre-Tolman model of a spherically symmetric non-rotating white hole with a few adjustable parameters is investigated. Comparison of calculated anisotropy in the Hubble flow and the CMB against …
In this paper we argue that modelling the black hole event horizon as a fuzzy sphere we can get a possible solution to the black hole information loss paradox.
In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper, we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about t…
We analyze scenarios of particle collisions in the metric of a nonextremal black hole that can potentially lead to ultrahigh energy $E_{c.m.}$ in their centre of mass frame. Particle 1 comes from infinity to the black hole horizon while particle 2 emerges from a white hole region. It is shown that unbounded $E_{c.m.}$ $\ $require that particle 2 pass close to the bifurcation point. The analogy with collisions inside the horizon is discussed.
We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let $M$ be a four dimensional asymptotically flat spacetime satisfying the averaged null energy conditio…
The physics at the event horizon resembles the behavior of waves in moving media. Horizons are formed where the local speed of the medium exceeds the wave velocity. We use ultrashort pulses in microstructured optical fibers to demonstrate the formation of an artificial event horizon in optics. We observed a classical optical effect, the blue-shifting of light at a white-hole horizon. We also show by theoretical calculations that such a system is capable of probing the quantum effects of horizons, in particular Hawking radiation.
The Einstein's equations with a negative cosmological constant admit solutions which are asymptotically anti-de Sitter space. Matter fields in anti-de Sitter space can be in stable equilibrium even if the potential energy is unbounded from below, violating the weak energy condition. Hence there is no fundamental reason that black hole's horizons should have spherical topology. In anti-de Sitter space the Einstein's equations admit black hole solutions where the horizon can be a Riemann surface with genus $g$. The case $g=0$ is the asymptotically anti-de Sitter black hole first studied by Hawki…
We prove that the domain of outer communication of a stationary, globally hyperbolic spacetime satisfying the null energy condition must be simply connected. Under suitable additional hypotheses, this implies, in particular, that each connected component of a cross-section of the event horizon of a stationary black hole must have spherical topology.
It is argued that a unitarity-violating but weakly CPT invariant superscattering matrix exists for leading-order large-$N$ dilaton gravity, if and only if one includes in the Hilbert space planckian ``thunderpop" excitations which create white holes. CPT apparently cannot be realized in a low-energy effective theory in which such states have been integrated out. Rules for computing the leading-large-$N$ superscattering are described in terms of quantum field theory on a single multiply-connected spacetime obtained by sewing the future (past) horizons of the original spacetime with the past (fu…
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…
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…
Geodesic completeness needs existence near the horizon of the black hole of "white hole" geodesics coming from the region inside of the horizon. Here we give the classification of all such geodesics with the energies $E/m \le 1$ for the Schwarzschild and Kerr's black hole. The collisions of particles moving along the "white hole" geodesics with those moving along "black hole" geodesics are considered. Formulas for the increase of the energy of collision in the centre of mass frame are obtained and the possibility of observation of high energy particles arriving from the black hole to the Earth…
Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid (in our case, water and silicon oil) as well as on the fluid depth and the wavelength regime. In some cases, it can be tuned to obtain a relativistic regime plus high-frequency dispersive effects. We discuss two types of ongoing analogue white-hole experiments: deep water waves propagating against a counter-current in a wave channel and shallow waves on a circular hydraulic jump.
