We study numerically gravitational collapse of a spherically symmetric instanton particle in five dimensions. We show that the late stages of the process are characterized by a nearly constant ``free energy'', the value of which matches (within numerical uncertainties) the value obtained from standard black-hole thermodynamics. This suggests a purely classical interpretation of the free energy of a black hole.
Gravitational collapse of a class of spherically symmetric stars are investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with gravitational collapse.
This note discusses possible quantum effects in the context of homogeneous flat FLRW and inhomogeneous LTB gravitational spherical collapse, which lead to bounce solutions.
The Cardy-Verlinde formula is analyzed in the contest of the gravitational collapse. Starting from the holographic principle, we show how the equations for a homogeneous and isotropic gravitational collapse describe the formation of the black hole entropy. Some comments on the role of the entangled entropy and the connection with the c-theorem are made.
We study a thermodynamic potential during the classical gravitational collapse of a 4D (3+1) massless scalar field to a Schwarzschild black hole in isotropic coordinates. We track numerically the function $F(t)=-dI/dt=-L$, where $I$ is the total action of matter plus gravitation, $L$ the total Lagrangian and $t$ is the time measured by a stationary clock at infinity. At late stages in the collapse, this function can be identified with the free energy $F=E-TS$ of the black hole where $E$ is the ADM mass, $T$ the Hawking temperature and $S$ the entropy. From standard black hole thermodynamics, t…
We study the effect of charge on gravitational collapse of inhomogeneous dust cloud in the Einstein, Gauss-Bonnet and Lovelock gravity. Dynamics of the collapsing shell is analyzed. The conditions for the occurrence of bounce during collapse are given. We also show that shell crossing occurs inevitably if the shell near the center is weakly charged.
We review here some recent developments on the issue of final fate of gravitational collapse within the framework of Einstein theory of gravity. The structure of collapsed object is discussed in terms of either a black hole or a singularity having causal connection with outside universe. Implications for cosmic censorship are discussed.
We present a solution to the vacuum Einstein Equations which represents a collapse of a gravitational wave in 5 dimensions. Depending on the focal length of the wave, the collapse results, either in a black string covered by a horizon, or in a naked singularity which can be removed.
Quantum gravity is treated as a stochastic quantization of the spacetime metric of general relativity. It is found that owing to the stochastic fluctuating behavior of the geometry, the singularity in gravitational collapse of a star has a zero probability density of occurring. Moreover, as a star collapses the probability density of a distant observer seeing an infinite red shift at the Schwarzschild radius of the star is zero. Therefore, there is a vanishing probability density of a black hole event horizon forming during gravitational collapse. A grey apparent event horizon forms during the…
The gravitational collapse in asymptotically AdS spacetimes is studied, using the differential configurational entropy (DCE). The DCE is shown to comply with the instability of the Einstein-Klein-Gordon system, leading to different stages in the route to turbulence and final black hole formation, including near the critical behavior.
We write the Hamiltonian for a gravitational spherically symmetric scalar field collapse with massive scalar field source, and we discuss the application of Wheeler De Witt equation as well as the appearence of time in this context. Using an Ansatz for Wheeler De Witt equation, solutions are discussed including the appearence of time evolution.
The thermal duality of E(8) x E(8) and SO(32) heterotic string theories may underpin a mechanism that would convert the kinetic energy of infalling matter during gravitational collapse to form a region of a hot string phase that would expel gravitational gradients. This phase would be the continuation of a Ginzburg-Landau like superconductor in the Euclidean regime. In this scenario, there would be no event horizon or singularity produced in gravitational collapse. Solutions are presented for excitations of the string vacuum that may form during gravitational collapse and drive the transition …
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under consideration and share similar forms as those in thermodynamic and geometrical phase transitions in condensed matter system. The properties of the scaling laws are discussed and some numerical checks are given.
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.
While studying the continual gravitational collapse of a massive matter cloud in general relativity towards examining collapse final states, an important issue is that of whether shell-crossing singularities can develop as the collapse evolves. We examine this here to show that for any spherically symmetric collapse in general, there is always a finite neighborhood of the center in which there are no shell-crossings taking place. It follows that in order to study the final genuine shell-focusing singularity of collapse where the physical radius of the matter cloud shrinks to a vanishing value,…
Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. This formalism utilizes well-established techniques used for classical collapse by choosing a convenient coherent state, and simulates the matter fields quantum mechanically. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classical results in gravitationa…
We study the charged scalar collapse in de Sitter spacetimes. With the electric charge, there is one more competitor to join the competition of dynamics in the gravitational collapse. We find that two factors can influence the electric charge. If we just adjust the charge conjugation, the electric charge effect is always perturbative at the black hole threshold. The electric charge can also be influenced by the initial conditions of perturbations. These initial parameters can be tuned to control the competition in dynamics and present us new and rich physics in the process of gravitational col…
We study the gravitational collapse of an inhomogeneous scalar field with quantum gravity corrections associated with singularity avoidance. Numerical simulations indicate that there is critical behaviour at the onset of black hole formation as in the classical theory, but with the difference that black holes form with a mass gap.
The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a "cosmic censor" which prevents any external observer from perceiving their existence. However, classical models describing the gravitational collapse usually results in strong curvature singularities, which can also remain "naked" for a finite amount of advanced time. This proceedings studies the modifications induced by Asymptotically Safe Gravity on the gravitational collapse of generic Vaidya spacetimes. It will be shown that, fo…
This paper shows a way of how one may resolve the non-unitarity problem in black-hole physics without modifications of the basic principles of local quantum field theory.
Based on a previously found general class of quantum improved exact solutions composed of non-interacting (dust) particles, we model the gravitational collapse of stars. As the modeled star collapses a closed apparent 3-horizon is generated due to the consideration of quantum effects. The effect of the subsequent emission of Hawking radiation related to this horizon is taken into consideration. Our computations lead us to argue that a total evaporation could be reached. The inferred global picture of the spacetime corresponding to gravitational collapse is devoid of both event horizons and she…
We study the spherically symmetric gravitational collapse of massless scalar matter field in asymptotic flat spacetime in $f(R)$ gravity. In the Einstein frame of $f(R)$ gravity, an additional scalar field arises due to the conformal transformation. We find that besides the usual competition between gravitational energy and kinetic energy in the process of gravitational collapse, the new scalar field brought by the conformal transformation adds one more competing force in the dynamical system. The dynamical competition can be controlled by tuning the amplitudes of the initial perturbations of …
We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically $AdS_D$ spacetimes for $D=4,5$. We conclude that spherically symmetric gravitational collapse in asymptotically $AdS$ spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as $ω^{-s}$ with the frequency, $ω$, and $s\approx 1.7\pm 0.1$.
We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.
Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. By choosing a convenient coherent state, this formalism taps into well-established techniques used for classical collapse and adds on the evolution of the mode functions of the quantum field operator. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classic…
We investigate the dynamics of homogeneous gravitational collapse of a massless vector field in the presence of a positive cosmological constant $Λ$. The corresponding density function $ρ(a)$ obtained for the massless vector field is inversely proportional to the fourth power of the scale factor $a (t)$. The variation of the scale factor shows that for $0\, \leΛ< 1$, we obtain the gravitational collapse of the vector fields leading singularity formation in a {\it finite} comoving time resulting in a {\it Blackhole} such that with increasing $Λ$, the singularity formation time, $t_s$ increases.…
This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (Roberts solution). The perturbation equations are derived and solved exactly. The perturbation spectrum is found to be not discrete, but occupying continuous region of the complex plane. The renormalization group calculation gives the value of the mass-scaling exponent equal to 1.
We describe a class of exactly soluble models for gravitational collapse in spherical symmetry obtained by patching dynamical spherically symmetric exterior spacetimes with cosmological interior spacetimes. These are generalizations of the Oppenheimer-Snyder type models to include classical and quantum scalar fields as sources for the interior metric, and null fluids with pressure as sources for the exterior metric. In addition to dynamical exteriors, the models exhibit other novel features such as evaporating horizons, and singularity avoidance without quantum gravity.
We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity.…
We examine the interplay between gravitational collapse and moduli stability in the context of black hole formation. We perform numerical simulations of the collapse using the double null formalism and show that the very dense regions one expects to find in the process of black hole formation are able to destabilize the volume modulus. We establish that the effects of the destabilization will be visible to an observer at infinity, opening up a window to a region in spacetime where standard model's couplings and masses can differ significantly from their background values.
Further to our consideration on trapped surfaces in gravitational collapse, where pressures were allowed to be negative while satisfying weak energy condition to avoid trapped surface formation, we discuss here several other attempts of similar nature in this direction. Certain astrophysical aspects are pointed out towards examining the physical realization of such a possibility in realistic gravitational collapse.
We discuss the status of both cosmological and black hole type singularities in the framework of the brane-world model of gravity. We point out that the Big Bang is not properly understood yet. We also show new features of the gravitational collapse on the brane, the most important being the production of dark energy during the collapse.
The functional Schrodinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the gravitational collapse. Truncating the degrees of freedom to a minisuperspace leads to an integro-differential Schrodinger equation. We define a "black hole" operator and find its eigenstates. The black hole operator does not commute with the Hamiltonian, leading to an energy-black holeness uncertainty relation. We discuss energy eigenstates and also obtain a partia…
This article gives an elementary overview of the end-state of gravitational collapse according to classical general relativity. The focus of discussion is the formation of black holes and naked singularities in various physically reasonable models of gravitational collapse. Possible implications for the cosmic censorship hypothesis are outlined.
We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $Λ$. The formalism is used for numerical simulations of gravitational collapse in four spacetime dimensions with negative $Λ$. We observe critical behaviour at the onset of black hole formation, and find that the critical exponent is independent of $Λ$.
We study quantum radiation emitted during the collapse of a quantized, gravitating, spherical domain wall. The amount of radiation emitted during collapse now depends on the wavefunction of the collapsing wall and the background spacetime. If the wavefunction is initially in the form of a sharp wavepacket, the expectation value of the particle occupation number is determined as a function of time and frequency. The results are in good agreement with our earlier semiclassical analysis and show that the quantum radiation is non-thermal and evaporation accompanies gravitational collapse.
We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=kρ$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final f…
Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to form a toroidal black hole. According to the analytical model presented, the collapsing matter absorbs energy in the form of radiation (be it scalar, neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon decompactification of one or two coordinates of the torus one gets collapsing solutions of cylindrical or planar matter onto black …
We study gravitational collapse of a spherically symmetric scalar field in Einstein-aether theory (general relativity coupled to a dynamical unit timelike vector field). The initial value formulation is developed, and numerical simulations are performed. The collapse produces regular, stationary black holes, as long as the aether coupling constants are not too large. For larger couplings a finite area singularity occurs. These results are shown to be consistent with the stationary solutions found previously.
This paper studies the whole process of gravitational collapse and accretion of a massless scalar field in asymptotically flat spacetime. Two kinds of initial configurations are considered. One is the initial data without black hole, the other contains a black hole. Under suitable initial conditions, we find that multi-horizon will appear, which means that the initial black hole formed by gravitational collapse or existing at the beginning will instantly expand and suddenly grow, rather than grows gradually in the accretion process. A new type of critical behavior is found around the instant e…
Gravity and thermal energy are universal phenomena which compete over the stabilization of astrophysical systems. The former induces an inward pressure driving collapse and the latter a stabilizing outward pressure generated by random motion and energy dispersion. Since a contracting self-gravitating system is heated up one may wonder why is gravitational collapse not halted in all cases at a sufficient high temperature establishing either a gravo-thermal equilibrium or explosion. Here, based on the equivalence between mass and energy, we show that there always exists a temperature threshold b…
This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.
We study the formation of black strings from a gravitational collapse of cylindrical dust clouds in the three-dimensional low-energy string theory. New junction conditions for the dilaton as well as two junction conditions for metrics and extrinsic curvatures between both regions of the clouds are presented. As a result, it is found that the collapsing dust cloud always collapses to a black string within a finite collapse time, and then a curvature singularity formed at origin is cloaked by an event horizon. Moreover, it is also shown that the collapse process can form a naked singularity with…
We study the collapse of a homogeneous braneworld dust cloud in the context of the various curvature correction scenarios, namely, the induced-gravity, the Gauss-Bonnet, and the combined induced-gravity and Gauss-Bonnet. In accordance to the Randall-Sundrum model, and contrary to four-dimensional general relativity, we show in all cases that the exterior spacetime on the brane is non-static.
A general solution to the $D=2$ 1-loop beta functions equations including tachyonic back reaction on the metric is presented. Dynamical black hole (classical) solutions representing gravitational collapse of tachyons are constructed. A discussion on the correspondence with the matrix-model approach is given.
We argue that $(0,1)$ heterotic string models with 4 non-heterotic spacetime dimensions may provide an instability of the vacuum to gravitational polarization in globally strong gravitational fields. This instability would be triggered during gravitational collapse by a non-local quantum switching process, and lead to the formation of regions of a high temperature broken symmetry phase which would be the equivalent in these string models of conventional black holes.
In this paper, we first generalize the definition of stationary universal horizons to dynamical ones, and then show that (dynamical) universal horizons can be formed from realistic gravitational collapse. This is done by constructing analytical models of a collapsing spherically symmetric star with finite thickness in Einstein-aether theory.
We study the collapse of a self-gravitating thick shell of bosons coupled to a scalar radiation field. Due to the non-adiabaticity of the collapse, the shell (quantum) internal degrees of freedom absorb energy from the (classical) gravitational field and are excited. The excitation energy is then emitted in the form of bursts of (thermal) radiation and the corresponding backreaction on the trajectory is estimated.
The general theory of matching conditions is developed for gravitational theories in two spacetime dimensions. Models inspired from general relativity and from string theory are considered. These conditions are used to study collapsing dust solutions in spacetimes with non-zero cosmological constant, demonstrating how two-dimensional black holes can arise as the endpoint of such collapse processes.
We investigate how braneworld gravity affects gravitational collapse and black hole formation by studying Oppenheimer-Snyder-like collapse on a Randall-Sundrum type brane. Without making any assumptions about the bulk, we prove a no-go theorem: the exterior spacetime on the brane cannot be static, which is in stark contrast with general relativity. We also consider the role of Kaluza-Klein energy density in collapse, using a toy model.
It is now a well established fact based on several observations that we live in a Universe dominated by dark energy. The most natural candidates for dark energy are fields in curved space-time. We develop the formalism to study the gravitational collapse of fields given any general potential. We apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting evolution equations which determine the time evolution of field configurations as well as the dynamics of spacetime.
A Hamiltonian treatment of the gravitational collapse of thin shells is presented. The direct integration of the canonical constraints reproduces the standard shell dynamics for a number of known cases. The formalism is applied in detail to three dimensional spacetime and the properties of the (2+1)-dimensional charged black hole collapse are further elucidated. The procedure is also extended to deal with rotating solutions in three dimensions. The general form of the equations providing the shell dynamics implies the stability of black holes, as they cannot be converted into naked singulariti…
