Radiating gravitational collapse with shear viscosity revisited

A new model is proposed to a collapsing radiating star consisting of an isotropic fluid with shear viscosity undergoing radial heat flow with outgoing radiation. In a previous paper we have introduced a function time dependent into the g _rr , besides the time dependent metric functions and . The aim of this work is to generalize this previous model by introducing shear viscosity and compare it to the non-viscous collapse. The behavior of the density, pressure, mass, luminosity and the effective adiabatic index is analyzed. Our work is compared to the case of a collapsing shearing fluid of a previous model, for a star with 6 . 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. An observer at infinity sees a radial point source radiating exponentially until reaches the time of maximum luminosity and suddenly the star turns off. The effective adiabatic index has a very unusual behavior because we have a non-adiabatic regime in the fluid due to the heat flow.     

Non-adiabatic radiative collapse of a relativistic star under different initial conditions

We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space t?=?constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.     

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.     

Gravitational collapse of phantom fluid in (2 + 1)-dimensions

In this paper, we solve Einsteins’ field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in (2 + 1)-dimensional spacetimes. Considering the case where the radial pressure vanishes, we show that there exists a solution that represents the gravitational collapse of an anisotropic fluid, and the collapse will finally form a black hole, even if the fluid is constituted by phantom energy.     

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).     

Pre-low-mass X-ray binaries containing a black hole: investigating a detection mechanism

This work investigates the feasibility of detecting close, detached, black hole-red dwarf binaries, which are expected to be evolutionary precursors of low-mass X-ray binaries (LMXBs). Although this pre-low-mass X-ray binary (pre-LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X-ray luminosity of black hole wind accretion in a pre-LMXB system could exceed the intrinsic X-ray luminosity of the red dwarf secondary star, thereby providing a detection mechanism. However, there is significant uncertainty regarding the efficiency of the conversion of gravitational potential energy to X-ray luminosity resulting from accretion onto a black hole, for example energy may be lost via advection across the event horizon. Still, sources with X-ray luminosities greater than that expected for a red dwarf star, but whose positions coincide with that of a red dwarf would represent candidate pre-LMXB systems. These candidates should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a black hole.      

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.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

Effects of CDTT model on the stability of spherical collapse in Palatini f(R) gravity

The objective of this paper is to study the stability of an adiabatic anisotropic collapsing sphere in the context of Palatini f(R) gravity. In this framework, we construct the collapse equation with the help of the contracted Bianchi identities of the effective as well as the usual energy-momentum tensor. The perturbation scheme is applied on the fluid variables which accordingly cause a perturbation on the Ricci scalar. We explore the instability ranges in the Newtonian and post-Newtonian regimes. It is concluded that the stability of the star is governed by adiabatic index Γ ₁, which depends on the energy density profile, anisotropic pressure and dark source terms of the chosen f(R) model. We also explore our results when f(R)→R.     

A neutron star collapse induced by a primordial black hole as the source of cosmological γ-ray bursts

A novel scenario is proposed for the origin of cosmological γ-ray bursts relating them with the induced collapse of an isolated neutron star under the action of a primordial black hole inside it. A mechanism is pointed out for black hole capturing into bounded orbits in a contracting protostellar cloud (which further evolves to a neutron star), and it is shown that this mechanism is most efficient in the pregalactic epoch. The qualitative results of neutrino transfer calculations are presented; these neutrinos originate from the quark phase transition in the nucleon matter which takes place in the accretion flow in the interior of the star. The neutrinos and antineutrinos escaping from a dense nucleon matter are degenerate and annihilate in the immediate vicinity of the star surface where an inverse temperature layer in the outstreaming electron-positron wind is produced. This layer acts as a natural barrier against baryon pollution and gives rise to a very high (≈ 10³) value of the Lorentz factor in the expanding plasma, in agreement with the observed energy and duration of the process. This makes it possible to explain the main properties of the γ-ray bursts. We also consider other important features of this scenario, including the predominantly extragalactic origin of the bursts, the apparent absence of the cosmological time dilation, the excess drop in the number of bursts—luminosity dependence for z>0.7, and the unlikely corrllation between the burst and the gravitational wave pulse.     

Star models with dark energy

We have constructed star models consisting of four parts: (i) a homogeneous inner core with anisotropic pressure (ii) an infinitesimal thin shell separating the core and the envelope; (iii) an envelope of inhomogeneous density and isotropic pressure; (iv) an infinitesimal thin shell matching the envelope boundary and the exterior Schwarzschild spacetime. We have analyzed all the energy conditions for the core, envelope and the two thin shells. We have found that, in order to have static solutions, at least one of the regions must be constituted by dark energy. The results show that there is no physical reason to have a superior limit for the mass of these objects but for the ratio of mass and radius.     

Magnetorotational Mechanism of the Explosion of Core-Collapse Supernovae

The idea of the magnetorotational explosion mechanism is that the energy of rotation of the neutron star formed in the course of a collapse is transformed into the energy of an expanding shock wave by means of a magnetic field. In the two-dimensional case, the time of this transformation depends weakly on the initial strength of the poloidal magnetic field because of the development of a magnetorotational instability. Differential rotation leads to the twisting and growth of the toroidal magnetic-field component, which becomes much stronger than the poloidal component. As a result, the development of the instability and an exponential growth of all field components occur. The explosion topology depends on the structure of the magnetic field. In the case where the initial configuration of the magnetic field is close to a dipole configuration, the ejection of matter has a jet character, whereas, in the case of a quadrupole configuration, there arises an equatorial ejection. In either case, the energy release is sufficient for explaining the observed average energy of supernova explosion. Neutrinos are emitted as the collapse and the formation of a rapidly rotating neutron star proceeds. In addition, neutrino radiation arises in the process of magnetorotational explosion owing to additional rotational-energy losses. If the mass of a newborn neutron star exceeds the mass limit for a nonrotating neutron star, then subsequent gradual energy losses may later lead to the formation of a black hole. In that case, the energy carried away by a repeated flash of neutrino radiation increases substantially. In order to explain an interval of 4.5 hours between the two observed neutrino signals from SN 1987A, it is necessary to assume a weakening of the magnetorotional instability and a small initial magnetic field (10⁹?10¹⁰ G) in the newly formed rotating neutron star. The existence of a black hole in the SN 1987A remnant could explain the absence of any visible pointlike source at the center of the explosion.     

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.     

Singularity-free dark energy star

We propose a model for an anisotropic dark energy star where we assume that the radial pressure exerted on the system due to the presence of dark energy is proportional to the isotropic perfect fluid matter density. We discuss various physical features of our model and show that the model satisfies all the regularity conditions and is stable as well as singularity-free.     

Relativistic equation of state of nuclear matter for supernova and neutron star

We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.     

Magnetic collapse of a neutron gas: Can magnetars indeed be formed?

A relativistic degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular to than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas. Taking this as a model for neutron stars, the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable neutron star pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and a meson condensate, a strange star, or a highly distorted black hole or black ”cigar”, but not a magnetar, if viewed as a superstrongly magnetized neutron star. However, we do not exclude the possibility of superstrong magnetic fields arising in supernova explosions which lead directly to strange stars. In other words, if any magnetars exist, they cannot be neutron stars. Received: 25 November 2002 / Revised version: 25 February 2003 / Published online: 5 May 2003     

Stability of a self-gravitating homogeneous resistive plasma

In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed.We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterion. The anisotropic collapse of a density contrast is sketched in detail, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced.The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancelation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different values of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

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.