We consider the causal structure of generalized uncharged McVittie spacetimes with increasing central mass $m (t)$ and positive Hubble factor $H (t)$. Under physically reasonable conditions, namely, a big bang singularity in the past, a positive cosmological constant and an upper limit to the central mass, we prove that the patch of the spacetime described by the cosmological time and areal radius coordinates is always geodesically incomplete, which implies the presence of event horizons in the spacetime. We also show that, depending on the asymptotic behavior of the $m$ and $H$ functions, the generalized McVittie spacetime can have a single black hole, a black-hole/white-hole pair or, differently from classic fixed-mass McVittie, a single white hole. A simple criterion is given to distinguish the different causal structures.
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…
This white paper summarizes recent progress in the cosmological bootstrap, an approach to the study of the statistics of primordial fluctuations from consistency with unitarity, locality and symmetry assumptions. We review the key ideas of the bootstrap method, with an eye towards future directions and ambitions of the program. Focusing on recent progress involving de Sitter and quasi-de Sitter backgrounds, we highlight the role of singularities and unitarity in constraining the form of the correlators. We also discuss nonperturbative formulations of the bootstrap, connections to anti-de Sitte…
We investigate the quantum deformation of the Wheeler--DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg--Weyl $U_q(h_4)$ group. We show that the event horizon area and the mass are quantized, degenerate, and bounded. The degeneracy of states indicates entangled quantum black hole/white hole states. Accordingly, quantum deformation provides a new framework to examine Einstein--Rosen wormhole solutions. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Sch…
It was previously argued that generalized uncertainty principle (GUP) with a positive parameter removes the Chandrasekhar limit. One way to restore the limit is by taking the GUP parameter to be negative. In this work we discuss an alternative method that achieves the same effect: by including a cosmological constant term in the GUP (known as "extended GUP" in the literature). We show that an arbitrarily small but nonzero cosmological constant can restore the Chandrasekhar limit. We also remark that if the extended GUP is correct, then the existence of white dwarfs gives an upper bound for the…
We briefly review the problem of generating cosmological flows of matter in GR (the genesis of universes), analyze models' shortcomings and their basic assumptions yet to be justified in physical cosmology. We propose a paradigm of cosmogenesis based on the class of spherically symmetric solutions with {\it integrable} singularity $r=0$. They allow for geodesically complete geometries of black/white holes, which may comprise space-time regions with properties of cosmological flows.
A theory of quantum gravity is expected to change profoundly our understanding of black holes. Quantum theory has already shown, as a first approximation, that a black hole slowly evaporates. Non-perturbative quantum gravity also predicts that such an object could metamorphose into a white hole, its time-reverse. In this thesis, we study the foundations of such a scenario and propose a mathematical model that includes the phenomenon of evaporation.
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.
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…
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 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.
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.
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 …
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)
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.
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…
The diameter of the apparent horizon, defined by the distance between furthest points on the horizon, in spacetimes with a positive cosmological constant $\varLambda$ has been investigated. It is established that the diameter of the apparent horizon on the totally umbilic partial Cauchy surface cannot exceed $2π/\sqrt{3\varLambda}$. Then, it is argued that arbitrarily long black strings cannot be formed in our universe.
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 …
We study the existence of analogue nonstationary spherically symmetric black holes. The prime example is the acoustic model (cf. [V], [U]). We consider also a more general class of metrics that could be useful in other physical models of analogue black and white holes. We give examples of the appearance of black holes and of disappearance of white holes. We also discuss the relation between the apparent and the event horizons for the case of analogue black holes. In the end we study the inverse problem of determination of black or white holes by boundary measurements for the spherically symmet…
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…
There have been a number of suggestions that the r = 0 singularity of a spherically symmetric (uncharged) evaporating black hole can be circumvented by a quantum transition to a white hole, which eventually releases all trapped quantum information, consistent with overall unitary evolution of the quantum fields. Some of these scenarios rely on loop quantum gravity to impose a minimum area of two-spheres, but are quite vague on how to deal with black hole evaporation, particularly its endpoint. In this paper I present a rather complete toy model for the evolution of the geometry and the effecti…
It is often argued that quantum gravitational correction to the Heisenberg's uncertainty principle leads to, among other things, a black hole remnant with finite temperature. However, such a generalized uncertainty principle also seemingly removes the Chandrasekhar limit, i.e., it permits white dwarfs to be arbitrarily large, which is at odds with astrophysical observations. We show that this problem can be resolved if the parameter in the generalized uncertainty principle is negative. We also discuss the Planck scale physics of such a model.
The notion that microparsec-scale black holes can be used to probe gigaparsec-scale physics may seem counterintuitive, at first. Yet, the gravitational observatory LISA will detect cosmologically-distant coalescing pairs of massive black holes, accurately measure their luminosity distance and help identify an electromagnetic counterpart or a host galaxy. A wide variety of new black hole studies and a gravitational version of Hubble's diagram become possible if host galaxies are successfully identified. Furthermore, if dark energy is a manifestation of large-scale modified gravity, deviations f…
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.
The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It adresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.
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…
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.
Recently Kaloper, Kleban and Martin reexamined the McVittie solution and argued, contrary to a very widely held belief, that the solution contains a black hole in an expanding universe. Here we corroborate their main conclusion but go on to examine, in some detail, a specific solution that asymptotes to the $Λ$CDM cosmology. We show that part of the boundary of the solution contains the inner bifurcation two - sphere of the Schwarzschild - de Sitter spacetime and so both the black and white hole horizons together form a partial boundary of this McVittie solution. We go on to show that the null…
Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized …
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 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…
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…
The apparent incompatibility between quantum theory and general relativity has long hampered efforts to find a quantum theory of gravity. The recently proposed positive formalism for quantum theory purports to remove this incompatibility. We showcase the power of the positive formalism by applying it to the black hole to white hole transition scenario that has been proposed as a possible effect of quantum gravity. We show how the characteristic observable of this scenario, the bounce time, can be predicted within the positive formalism, while a traditional S-matrix approach fails at this task.…
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…
We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. We implement the quantum hydrodynamic equations and carry out numerical simulations. As a model of a white dwarf star, we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. Due to nonlinear effects, the accretion disk originated from the white dwarf becomes fragmented …
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…
Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measu…
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 …
The thermodynamics of black holes is discussed for the case, when the Newton constant $G$ is not a constant, but is the thermodynamic variable. This gives for the first law of the Schwarzschild black hole thermodynamics: $dS_\text{BH}= -AdK + \frac{dM}{T_\text{BH}}$, where the gravitational coupling $K=1/4G$, $M$ is the black hole mass, $A$ is the area of horizon, and $T_\text{BH}$ is Hawking temperature. From this first law it follows that the dimensionless quantity $M^2/K$ is the adiabatic invariant, which in principle can be quantized if to follow the Bekenstein conjecture. From the Euclide…
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…
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…
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…
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…
Black holes provide a window into the microscopic structure of spacetime in quantum gravity. Recently the quantum information contained in Hawking radiation has been calculated, verifying a key aspect of the consistency of black hole evaporation with quantum mechanical unitarity. This calculation relied crucially on recent progress in understanding the emergence of bulk spacetime from a boundary holographic description. Spacetime wormholes have played an important role in understanding the underpinnings of this result, and the precision study of such wormholes, in this and other contexts, has …
