Rebounce and black hole formation in a gravitational collapse model with vanishing radial pressure

We examine here spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of the initial parameters which are initial density, tangential pressure and velocity profile of the cloud. A threshold of black hole formation is observed near which a scaling relation is obtained for the mass of black hole, assuming initial profiles to be smooth. The similarities in the behaviour of this model at the onset of black hole formation with that of numerical critical behaviour in other collapse models are indicated.     

Charged black holes in phantom cosmology

In the classical relativistic regime, the accretion of phantom-like dark energy onto a stationary black hole reduces the mass of the black hole. We have investigated the accretion of phantom energy onto a stationary charged black hole and have determined the condition under which this accretion is possible. This condition restricts the mass-to-charge ratio in a narrow range. This condition also challenges the validity of the cosmic-censorship conjecture since a naked singularity is eventually produced due to accretion of phantom energy onto black hole.     

Charged boson stars and black holes

We consider boson stars and black holes in scalar electrodynamics with a V-shaped scalar potential. The boson stars come in two types, having either ball-like or shell-like charge density. We analyze the properties of these solutions and determine their domains of existence. When mass and charge become equal, the space–times develop a throat. The shell-like solutions need not be globally regular, but may possess a horizon. The space–times then consist of a Schwarzschild-type black hole in the interior, surrounded by a shell of charged matter, and thus a Reissner–Nordström-type space–time in the exterior. These solutions violate black hole uniqueness. The mass of the black hole solutions is related to the mass of the regular shell-like solutions by a mass formula of the type first obtained within the isolated horizon framework.     

Exact solutions for shells collapsing towards a pre-existing black hole

The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well-known “frozen star” paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this Letter. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no “frozen star” is formed for an external observer as matter falls towards a black hole. Therefore, we predict that only gravitational wave radiation can be produced in the final stage of the merging process of two coalescing black holes. Our results also indicate that for the clock of an external observer, matter, after crossing the event horizon, will never arrive at the “singularity” (i.e. the exact center of the black hole), i.e., for all black holes with finite lifetimes their masses are distributed within their event horizons, rather than concentrated at their centers. We also present a worked-out example of the Hawking's area theorem.     

Will black holes eventually engulf the Universe?

The Babichev–Dokuchaev–Eroshenko model for the accretion of dark energy onto black holes has been extended to deal with black holes with non-static metrics. The possibility that for an asymptotic observer a black hole with large mass will rapidly increase and eventually engulf the Universe at a finite time in the future has been studied by using reasonable values for astronomical parameters. It is concluded that such a phenomenon is forbidden for all black holes in quintessential cosmological models.     

Accretion of Phantom Energy and Generalized Second Law of Thermodynamics for Einstein-Maxwell-Gauss-Bonnet Black Hole

We have investigated the accretion of phantom energy onto a 5-dimensional extreme Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole. It is shown that the evolution of the EMGB black hole mass due to phantom energy accretion depends only on the pressure and density of the phantom energy and not on the black hole mass. Further we study the generalized second law of thermodynamics (GSL) at the event horizon and obtain a lower bound on the pressure of the phantom energy.     

Generalized second law of thermodynamics for a phantom energy accreting BTZ black hole

In this paper, we have studied the accretion of phantom energy on a (2 + 1)-dimensional stationary Banados–Teitelboim–Zanelli (BTZ) black hole. It has already been shown by Babichev et al. that for the accretion of phantom energy onto a Schwarzschild black hole, the mass of black hole would decrease and the rate of change of mass would be dependent on the mass of the black hole. However, in the case of (2 + 1)-dimensional BTZ black hole, the mass evolution due to phantom accretion is independent of the mass of the black hole and is dependent only on the pressure and density of the phantom energy. We also study the generalized second law of thermodynamics at the event horizon and construct a condition that puts an lower bound on the pressure of the phantom energy.     

Horizonless,singularity-free,compact shells satisfying NEC

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose’s singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.     

Evolution of a Schwarzschild black hole in phantom-like Chaplygin gas cosmologies

In the classical relativistic regime, the accretion of phantom energy onto a black hole reduces the mass of the black hole. In this context, we have investigated the evolution of a Schwarzschild black hole in the standard model of cosmology using the phantom-like modified variable Chaplygin gas and the viscous generalized Chaplygin gas. The corresponding expressions for accretion time scale and evolution of mass have been derived. Our results indicate that the mass of the black hole will decrease if the accreting phantom Chaplygin gas violates the dominant energy condition and will increase in the opposite case. Thus, our results are in agreement with the results of Babichev et al. who first proposed this scenario.     

Phantom energy accretion onto a black hole in Horava-Lifshitz gravity

In this Letter,we examine the phantom energy accretion onto a Kehagias-Sfetsos black hole in Horava-Lifshitz gravity.To discuss the accretion process onto the black hole,the equations of phantom flow near the black hole have been derived.It is found that mass of the black hole decreases because of phantom accretion.We discuss the conditions for critical accretion.Graphically,it has been found that the critical accretion phenomena is possible for different values of parameters.The results for the Schwarzschild black hole can be recovered in the limiting case.     

Thin charged shells and the violation of the third law of black hole mechanics

The collapse of an infinitely thin spherical shell of charged matter, which surrounds a spherically symmetric black hole or has a flat interior, is analyzed in connection with the laws of black hole mechanics and the cosmic censorship hypothesis. An effective potential is introduced to describe the motion of the shell. The process, proposed by Farrugia and Hajicek as a counterexample to the third law, is discussed and generalized to the case of nondust shells.     

Accretion onto Charged Black Holes in Einstein and Massive Theories of Gravity *

The accretion process is being investigated onto some important black holes such as Born-Infeld-AdS black hole, non-linear charged black hole solution in AdS space-time and Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrodynamics. We find out the relations of radial velocity, energy density and change of mass for mention black holes and analyze their behavior graphically for different values of equation of state parameters $\omega$. We also examine the relations for critical speed for these black holes. It is observed that for different state parameters different fluids exhibit different evolutions in black holes backgrounds. The energy density of some fluids is negative or positive near the black hole while other fluids become cause to increase or decrease in black hole mass.     

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.     

Gedanken experiments to destroy a black hole

It is widely believed that the complete gravitational collapse of a body always results in a black hole (i.e., “naked singularities” can never be produced) and that all black holes eventually “settled down” to Kerr-Newman solutions. An important feature of the Kerr-Newman black holes is that they satisfy relation m² ? a² + e² where m is the mass of the black hole, e is its charge, $\text{a =}\text{J}\text{m}$ is its angular momentum per unit mass and geometrized units G = c = 1 are used. (For m² <a² + e² the Kerr-Newman solutions describe naked singularities.) In this paper, we test the validity of the above conjectures on gravitational collapse by attempting to create a spacetime with m² <a² + e² starting with a Kerr-Newman black hole with m² = a² + e². Such a spacetime would either have to be a new black hole solution or a “naked singularity,” in violation of the above conjectures. In the first gedanken experiment we attempt to make the black hole capture a test particle having large charge and orbital angular momentum compared with energy. In the second gedanken experiment we attempt to drop into the black hole a spinning test body having large spin to mass ratio. In both cases we find that bodies which would cause violation of m² ? a² + e² will not be captured by the black hole, and, thus, we cannot obtain m² <a² + e², although we can come arbitrarily close in the sense that m² = a² + e² can be maintained in these processes.     

Constant curvature f(R) gravity minimally coupled with Yang–Mills field

In this work, we have studied accretion of the dark energies in new variable modified Chaplygin gas (NVMCG) and generalized cosmic Chaplygin gas (GCCG) models onto Schwarzschild and Kerr?CNewman black holes. We find the expression of the critical four velocity component which gradually decreases for the fluid flow towards the Schwarzschild as well as the Kerr?CNewman black hole. We also find the expression for the change of mass of the black hole in both cases. For the Kerr?CNewman black hole, which is rotating and charged, we calculate the specific angular momentum and total angular momentum. We showed that in both cases, due to accretion of dark energy, the mass of the black hole increases and angular momentum increases in the case of a Kerr?CNewman black hole.     

On the Tidally Induced Gravitational Collapse of a Particle Cluster

An important issue in the dynamics of neutron star binaries is whether tidal interaction can cause the individual stars to collapse into black holes during inspiral. To understand this issue better, we study the dynamics of a cluster of collisionless particles orbiting a non-rotating black hole, which is part of a widely separated circular binary. The companion body's electric- and magnetic-type tidal fields distort the black hole and perturb the cluster, eventually causing the cluster to collapse into the hole as the companion spirals in under the influence of gravitational radiation reaction. We find that magnetic-type tidal forces do not significantly influence the evolution of the cluster as a whole. However, individual orbits can be strongly affected by these forces. For example, some orbits are destabilized due to the addition of magnetic-type tidal forces. We find that the most stable orbits are close to the companion's orbital plane and retrograde with respect to the companion's orbit.     

Black Holes in Bulk Viscous Cosmology

We investigate the effects of the accretion of phantom energy with non-zero bulk viscosity onto a Schwarzschild black hole and show that black holes accreting viscous phantom energy will lose mass rapidly compared to the non-viscous case. When matter is incorporated along with the phantom energy, the black holes meet with the same fate as bulk viscous forces dominate matter accretion. If the phantom energy has large bulk viscosity, then the mass of the black hole will reduce faster than in the small viscosity case.     

Rotating dirty black hole and its shadow

In this paper, we examine the effect of dark matter to a Kerr black hole of mass m. The metric is derived using the Newman-Janis algorithm, where the seed metric originates from the Schwarzschild black hole surrounded by a spherical shell of dark matter with mass M and thickness Δr_s. The seed metric is also described in terms of a piecewise mass function with three different conditions. Specializing in the non-trivial case where the observer resides inside the dark matter shell, we analyzed how the effective mass of the black hole environment affects the basic black hole properties. A high concentration of dark matter near the rotating black hole is needed to have considerable deviations on the horizons, ergosphere, and photonsphere radius. The time-like geodesic, however, shows more sensitivity to deviation even at very low dark matter density. Further, the location of energy extraction via the Penrose process is also shown to remain unchanged. With how the dark matter distribution is described in the mass function, and the complexity of how the shadow radius is defined for a Kerr black hole, deriving an analytic expression for Δr_s as a condition for notable dark matter effects to occur remains inconvenient.