Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.     

Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) (Oppenheimer and Snyder in Phys Rev 56:455, 1939; Datt in Zs f Phys 108:314, 1938). This extends a previous result on tangential pressures (Joshi and Malafarina Phys Rev D 83:024009, 2011) to the physically more realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.     

Radiating gravitational collapse with an initial inhomogeneous energy density distribution

A new model is proposed to a collapsing star consisting of an initial inhomogeneous energy density and anisotropic pressure fluid with shear, radial heat flow and outgoing radiation. In previous papers one of us has always assumed an initial star with homogeneous energy density. The aim of this work is to generalize the previous models by introducing an initial inhomogeneous energy density and compare it to the initial homogeneous energy density collapse model. We will show the differences between these models in the evolution of all physical quantities that characterizes the gravitational collapse. The behavior of the energy density, pressure, mass, luminosity and the effective adiabatic index is analyzed. The pressure of the star, at the beginning of the collapse, is isotropic but due to the presence of the shear the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast of the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. In contrast of the former model where the luminosity also increases exponentially, reaching a maximum and after it decreases until the formation of the black hole. The effective adiabatic index is always positive without any discontinuity in contrast of the former model where there is a discontinuity around the time of maximum luminosity. The collapse is about three thousand times slower than in the case where the energy density is initially homogeneous.     

Role of Modified Chaplygin Gas as an Unified Dark Matter-Dark Energy Model in Collapsing Spherically Symmetric Dust Cloud

In this work gravitational collapse of a spherical dust cloud in the background of unified dark matter-dark energy model in the form of modified Chaplygin gas is studied. It is found that invisible matter (dark matter-dark energy) alone in the form of modified Chaplygin gas forms black hole. Also when both components of the fluid are present then the collapse favours the formation of black hole in cases the invisible matter dominates over ordinary dust. The conclusion is totally opposite to the usually known results.     

On the occurrence of naked singularity in spherically symmetric gravitational collapse

Generalizing earlier results of [1], we analyze here the spherically symmetric gravitational collapse of a matter cloud with a general form of matter for the formation of a naked singularity. It is shown that this is related basically to the choice of initial data to the Einstein field equations, and would therefore occur in generic situations from regular initial data within the general context considered here, subject to the matter satisfying the weak energy condition. The condition on initial data which leads to the formation of black hole is also characterized.     

On the Global Visibility of the Singularity in Quasi-Spherical Collapse

We analyze here the issue of local versus global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions for when a singularity will be only locally naked, rather than being globally visible, thus preserving the weak censorship hypothesis. The conditions for the formation of a black hole or a naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is that the singularity in Szekeres spacetimes can be directionally naked.     

Perturbative Approach to the Inner Structure of a Rotating Black Hole

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an empty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Kerr. We shall discuss the generalization of Price's analysis (regarding the latetime asymptotic decay of perturbations outside the black hole) from Schwarzschild to Kerr, and present preliminary results. We then consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbitrarily) small initial perturbations. This, we argue, justifies the attempt to apply the small-perturbation approach to the black hole's interior. We discuss the physical significance of this late-time region. We shall also outline the strategy we use for evolving the perturbations from the event horizon to the inner horizon.     

Space-borne gravitational wave observatories

An overview of our current knowledge of black seed formation models following their growth history over cosmic time is presented. Both light seed formation channels remnants of the first stars and the more massive direct collapse seed formation scenarios are outlined. In particular, the focus is on the implications of these various scenarios and what these initial conditions imply for the highest redshift black holes, the local black hole population, the highest mass black holes at each epoch and the low mass end of the black hole mass function all of which are currently observed. The goal is to present a broad and comprehensive picture of the current status; the open questions and challenges faced by black hole growth models in matching current observational data and the prospects for future observations that will help discriminate between competing models.     

Gravitational Collapse of Dust Cloud with Dark Energy

In this paper, we have investigated the gravitational collapse of a spherically symmetric star with anisotropic pressure, made of a dust fluid and dark energy with equations of state p _t =wρ and p _r =kρ, {(k+2w)<?1}. We have considered three cases. First with dust cloud, the second with dark energy and the third with both dust cloud and dark energy without interaction. The effects of dark energy on the gravitational collapse has been studied. It is found that when only dark energy is present, black hole can never be formed. When both dust cloud and dark energy are present, a black hole is formed. This work provides a generalization of the work by Cai and Wang for isotropic pressure to anisotropic pressure (Cai and Wang in Phys. Rev. D 73:063005, 2006).     

Dynamics of phantom matter

A spherically symmetric evolution model of self-gravitating matter with the equation of state p = ?(1 + δ)? (where δ = const) is considered. The equations of the model are written in the frame of reference co-moving with matter. A criterion for the existence and formation of a horizon is defined. Part of the Einstein equations is integrated analytically. The initial conditions and the constraints imposed on these conditions in the presence of a horizon are determined. For small δ, an analytic solution to spherically symmetric time-dependent Einstein equations is obtained. Conditions are determined under which the dynamics of matter changes from collapse to expansion. Characteristic times of the evolution of the system are evaluated. It is proved that the accretion of phantom matter (for δ > 0) onto a black hole leads to the decreases of the horizon radius of the black hole (i.e., the black hole is dissolved).     

Analytical solutions for black-hole critical behaviour

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.     

Primordial black hole formation by stabilized embedded strings in the early universe

Primordial black hole formation by cosmic string collapses is reconsidered in the case where the winding number of the string is larger than unity. The line energy density of a multiple winding string becomes greater than that of a single winding string so that the probability of black hole formation by string collapse during loop oscillation would be strongly enhanced. Moreover, this probability could be affected by changes in gravity theory due to large extra dimensions based on the brane universe model. In addition, a wider class of strings which are stable compared to conventional cosmic strings can contribute to such a scenario. Although the production of the multiple winding defect is suppressed and its number density should be small, the enhancement of black hole formation by the increased energy density may provide a large number of evaporating black holes in the present universe which gives more stringent constraints on the string model compared to the ordinary string scenario.     

Formation and evaporation of nonsingular black holes

Regular (nonsingular) space-times are given that describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region. The static region is Bardeen-like, supported by finite density and pressures, vanishing rapidly at large radius and behaving as a cosmological constant at small radius. The dynamic regions are Vaidya-like, with ingoing radiation of positive-energy flux during collapse and negative-energy flux during evaporation, the latter balanced by outgoing radiation of positive-energy flux and a surface pressure at a pair creation surface. The black hole consists of a compact space-time region of trapped surfaces, with inner and outer boundaries that join circularly as a single smooth trapping horizon.     

Gravastars and black holes of anisotropic dark energy

Dynamical models of prototype gravastars made of anisotropic dark energy are constructed, in which an infinitely thin spherical shell of a perfect fluid with the equation of state p = (1 − γ)σ divides the whole spacetime into two regions, the internal region filled with a dark energy fluid, and the external Schwarzschild region. The models represent “bounded excursion” stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes. Here we show, for the first time in the literature, a model of gravastar and formation of black hole with both interior and thin shell constituted exclusively of dark energy. Besides, the sign of the parameter of anisotropy (p _t − p _r ) seems to be relevant to the gravastar formation. The formation is favored when the tangential pressure is greater than the radial pressure, at least in the neighborhood of the isotropic case (ω = −1).     

Black Holes and Inflation

A model for black hole collapse and evaporation in which the black hole is supposed to be an excited state of one of the Planck black holes pervading the structure of spacetime is discussed. By assuming a Coleman-Weinberg gravitational effective potential for a scalar field inside the collapse matter, it is shown that the black hole state cannot be attained neither through bubble tunneling nor by the rolling down of the field.     

Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

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 mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.     

Spherical Gravitational Collapse: Tangential Pressure and Related Equations of State

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of the Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.     

Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes

According to prevailing theory, relativistic degenerate stars with masses beyond the Chandrasekhar and Oppenheimer–Volkoff (OV) limits cannot achieve hydrostatic equilibrium through either electron or neutron degeneracy pressure and must collapse to form stellar black holes. In such end states, all matter and energy within the Schwarzschild horizon descend into a central singularity. Avoidance of this fate is a hoped-for outcome of the quantization of gravity, an as-yet incomplete undertaking. Recent studies, however, suggest the possibility that known quantum processes may intervene to arrest complete collapse, thereby leading to equilibrium states of macroscopic size and finite density. I describe here one such process which entails pairing (or other even-numbered association) of neutrons (or constituent quarks in the event of nucleon disruption) to form a condensate of composite bosons in equilibrium with a core of degenerate fermions. This process is analogous to, but not identical with, the formation of hadron Cooper pairs that give rise to neutron superfluidity and proton superconductivity in neutron stars. Fermion condensation to composite bosons in a star otherwise destined to collapse to a black hole facilitates hydrostatic equilibrium in at least two ways: (1) removal of fermions results in a decrease in the Fermi level which stiffens the dependence of degeneracy pressure on fermion density, and (2) phase separation into a fermionic core surrounded by a self-gravitating condensate diminishes the weight which must be balanced by fermion degeneracy pressure. The outcome is neither a black hole nor a neutron star, but a novel end state, a “fermicon star,” with unusual physical properties.     

Formation of Gyrs old black holes in the centers of galaxies within the Lema?tre–Tolman model

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema?tre–Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass 3.2 × 10⁹ M⊙. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the ΛCDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the Ω _m and Ω_Λ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr.     

Radiating shear-free gravitational collapse with charge

We present here a new shear free model for the gravitational collapse of a spherically symmetric charged body. We propose a dissipative contraction with radiation emitted outwards represented by the Vaidya–Reissner–Nordström metric. The Einstein field equations, using the junction conditions and an ansatz, are integrated numerically. A check of the energy conditions is also performed. We obtain that the charge delays the Reissner–Nordström black hole formation and it can even prevent the collapse.