We present a dynamical toy model for an expanding universe inside a black hole. The model is built by matching a spherically symmetric collapsing matter cloud to an expanding Friedmann-Robertson-Walker universe through a phase transition that occurs in the quantum-gravity dominated region, here modeled with semi-classical corrections at high density. The matching is performed on a space-like hyper-surface identified by the co-moving time at which quantum-gravity induced effects halt collapse. The purpose of the model is to suggest a possible reconciliation between the observation that black holes are well described by the classical solutions and the fact that the theoretical resolution of space-time singularities leads to a bounce for the collapsing matter.
We explore a simple toy model of interacting universes to establish that a small baby universe could become large ($\gg$ Planck length) if a third quantization mechanism is taken into account.
General relativity predicts that the inner horizon of an astronomically realistic rotating black hole is subject to the mass inflation instability. The inflationary instability acts like a gravity-powered particle accelerator of extraordinary power, accelerating accreted streams of particles along the principal outgoing and ingoing null directions at the inner horizon to collision energies that would, if nothing intervened, typically exceed exponentially the Planck energy. The inflationary instability is fueled by ongoing accretion, and is occurring inevitably in essentially every black hole i…
Unlike three-dimensional Einstein gravity, three-dimensional massive gravity admits asymptotically de Sitter space (dS) black hole solutions. These black holes present interesting features and provide us with toy models to study the dS/CFT correspondence. A remarkable property of these black holes is that they are always in thermal equilibrium with the cosmological horizon of the space that hosts them. This invites us to study the thermodynamics of these solutions within the context of dS/CFT. We study the asymptotic symmetry group of the theory and find that it indeed coincides with the local…
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…
We address the question of universes inside a $Λ$ black hole which is described by a spherically symmetric globally regular solution to the Einstein equations with a variable cosmological term $Λ_{μν}$, asymptotically $Λg_{μν}$ as $r\to 0$ with $Λ$ of the scale of symmetry restoration. Global structure of spacetime contains an infinite sequence of black and white holes, vacuum regular cores and asymptotically flat universes. Regular core of a $Λ$ white hole models the initial stages of the Universe evolution. In this model it starts from a nonsingular nonsimultaneous big bang, which is followe…
We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole which is perturbed nonlinearly by a self-gravitating, spherical scalar field. The latter grows logarithmically with advanced time along an outgoing characteristic hypersurface. We find that for that class of perturbations a portion of the Cauchy horizon survives as a non-central, null singularity.
A magnetic field connecting a Kerr black hole to a disk rotating around it can extract energy and angular momentum from the black hole and transfer them to the disk if the black hole rotates faster than the disk. The energy can be dissipated and radiated away by the disk, which makes the disk shine without the need of accretion. In this paper we present a toy model for the magnetic connection: a single electric current flowing around a Kerr black hole in the equatorial plane generates a poloidal magnetic field which connects the black hole to the disk. The rotation of the black hole relative t…
The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quan…
Inspired by a recent model of Osuga and Page, we propose an explicitly unitary fermionic toy model for transferring information from a black hole to the outgoing radiation. The model treats the unitary evolution as a composition of the Hawking pair creation outside the black hole and of pair annihilation inside the black hole.
We show that Weyl-invariant dilaton gravity provides a description of black holes without classical spacetime singularities. Singularities appear due to ill-behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are: (1) singularities signal a phase transition from broken to unbroken phase of Weyl symmetry, (2) instead of a singularity there is a "baby-universe" or a white hole inside a black hole, (3) in the baby universe scenario there is a critical mass after which reduc…
The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subaddditivity has sorted out the possible resolutions into three sharp categories: (A) No new physics at $r\gg l_p$; this necessarily implies remnants/information loss. A realization of remnants is given by a baby Universe attached near $r\sim 0$. (B) Violation of the `no-hair' theorem by nontrivial effects at the horizon $r\sim M$. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (C) Having the vacuum at the horizon, …
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spher…
Phonon creation inside the horizons of acoustic black holes is investigated using two simple toy models. It is shown that, unlike what occurs in the exterior regions, the spectrum is not thermal. This non-thermality is due to the anomalous scattering that occurs in the interior regions.
We investigate dark and visible matter distribution in the Coma cluster in the case of the Navarro-Frenk-White (NFW) profile. A toy model where all galaxies in the cluster are concentrated inside a sphere of an effective radius $R_{\mathrm{eff}}$ is considered. It enables us to obtain the mean velocity dispersion as a function of $R_{\mathrm{eff}}$. We show that, within the observation accuracy of the NFW parameters, the calculated value of $R_{\mathrm{eff}}$ can be rather close to the observable cutoff of the galaxy distribution. Moreover, the comparison of our toy model with the observable d…
We describe the dynamics of a cosmological term in the spherically symmetric case by an r-dependent second rank symmetric tensor Λ_{μν} invariant under boosts in the radial direction. The cosmological tensor Λ_{μν} represents the extension of the Einstein cosmological term Λg_{μν} which allows a cosmological constant be variable. This possibility is based on the Petrov classification scheme and Einstein field equations in the spherically symmetric case. The inflationary equation of state is satisfied by the radial pressure p_r^Λ=-ρ^Λ. The tangential pressure is calculated from the conservation…
A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein's area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particul…
It is often said that there is no gravity theory based on local action principles giving rise to firewall black hole solutions. Additionally, Guo and Mathur 2022 (2205.10921) have cast doubt on the observability of firewall echoes due to closed trapped surface produced by backreaction of macroscopic in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton action as a toy model that serves as counterexample to these assertions. Actions with Maxwell and dilaton fields emerge from several fundamental theories, such as the low energy limit of (super) string theory or Kaluza-Klein …
The electromagnetic field around a Kerr black hole inside a current loop is sometimes used as the basis of a toy model for discussing the properties of particle orbits near astrophysical black holes. The motivation for the present paper is to correct the published solution to Maxwell's equations with a charged current loop. Dipole approximations and closed-form expressions in the extreme Kerr limit are also presented. Using the corrected solution, it turns out that imposing a vanishing electromotive force produces a loop with a potential which is finite everywhere outside the black hole. Ring …
We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero…
Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the sing…
We present results from a numerical study of rotating black hole formation in 3-dimensional asymptotically anti-de Sitter (AdS) spacetime, focusing on the structure of the black hole interior. While black holes in $AdS_3$ are of theoretical interest for a wide variety of reasons, we choose to study this system primarily as a toy model for astrophysical (4-dimensional) black holes formed from gravitational collapse. We investigate the effect of angular momentum on the geometry inside the event horizon, and see qualitative changes in the interior structure as a function of the spin parameter. Fo…
We continue the programme of exploring the means of holographically decoding the geometry of spacetime inside a black hole using the gauge/gravity correspondence. To this end, we study the behaviour of certain extremal surfaces (focusing on those relevant for equal-time correlators and entanglement entropy in the dual CFT) in a dynamically evolving asymptotically AdS spacetime, specifically examining how deep such probes reach. To highlight the novel effects of putting the system far out of equilibrium and at finite volume, we consider spherically symmetric Vaidya-AdS, describing black hole fo…
Compact stars satisfy certain no-hair relations through which their multipole moments are given by their mass, spin and quadrupole moment. These relations are approximately independent of their equation of state, relating pressure to density. Such relations are similar to the black hole no-hair theorems, but these possess event horizons inside which information that led to their formation can hide. Compact stars do not possess horizons, so whether their no-hair relations are related to the black hole ones is unclear. We investigate how the two relations are related by studying relations among …
A reformulation of the calculation of the semi-classical energy-momentum tensor on a Schwarzschild background, the Bousso covariant entropy bound, and the ER=EPR conjecture of Maldacena and Susskind taken together suggest a scenario for the evaporation of a large spherically symmetric black hole formed in gravitational collapse in which 1) the classical r = 0 singularity is replaced by an initially small non-singular core inside an inner apparent horizon, 2) the radius of the core grows with time due to the increasing entanglement between Hawking radiation quanta outside the black hole and the…
In this work, we focus on the situation where a significant amount of matter could be located close to the event horizon of the central black hole and how it affects the gravitational lensing signal. We consider a simple toy model where the matter is concentrated in the rather small region between the inner photon sphere associated with the mass of central black hole and outer photon sphere associated with the total mass outside. If no photon sphere is present inside the matter distribution, then effective potential displays an interesting trend with maxima at inner and outer photon sphere, wi…
In this paper we study gravitational lensing in the strong field limit from the perspective of cosmic censorship, to investigate whether or not naked singularities, if at all they exist in nature, can be distinguished from black holes. We study the gravitational lensing in the strong field regime in the JMN spacetime, a spherically symmetric geometry that contains a naked singularity and which matches smoothly with Schwarzschild metric beyond a finite radius. This metric is a toy model which was shown recently to be the end state of gravitational collapse. In the presence of the photon sphere …
