Spherical Gravitational Collapse Research Articles

Création de fermions à l'horizon d'un trou noir chargé

We investigate the quantum state of the Dirac field at the horizon of a charged black-hole formed by a spherical gravitational collapse. We prove this state satisfies a KMS condition with the Hawking temperature and the chemical potential associated with the mass and the charge of the black-hole. Moreover, the fermions with charge of same sign to that of the black-hole are emitted more readily than those of opposite charge.

A characterization of the central shell-focusing singularity in spherical gravitational collapse

We give a characterization of the central shell-focusing curvature singularity that can form in the spherical gravitational collapse of a bound matter distribution obeying the dominant energy condition. This characterization is based on the limiting behaviour of the mass function in the neighbourhood of the singularity. Depending on the rate of growth of the mass as a function of the area radius R, the singularity may be either covered or naked. The singularity is naked if this growth rate is slower than R, covered if it is faster than R, and either naked or covered if the growth rate is the same as R.

Gravitational collapse of perfect fluid

The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similarity, the formation of black holes always starts with a finite non-zero mass. The packet is usually accompanied by a thin matter shell. The effects of the shell on the collapse are also studied.

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 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.

The Instability of Naked Singularities in the Gravitational Collapse of a Scalar Field

One of the fundamental unanswered questions in the general theory of relativity is whether \naked singularities, that is singular events which are visible from inflnity, may form with positive probability in the process of gravitational collapse. The conjecture that the answer to this question is in the negative has been called \cosmic censorship. The present paper, which is a continuation of the work in [1], [2], [3] and [4] addresses this question in the context of the spherical gravitational collapse of a scalar fleld. The problem of a spherically symmetric self-gravitating scalar fleld is formulated in terms of a 2-dimensional quotient space-time manifold Q with boundary (see [1]). The boundary ofQ corresponds to the set of flxed points of the group action, the center of symmetry, which is a timelike geodesic i. The manifoldQ is endowed with a Lorentzian metric gab, an area radius function i‚ @ i‚ @ @r

Spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state . It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive k there is a finite region near the centre which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be spacelike. If this collapsing shell exists it might, in turn, be surrounded by a second expanding region. For negative k the entire object collapses inwards, but any singularities that could arise are not naked, except possibly at the centre. Thus the nature of the evolution is very different from that of dust, even when k is infinitesimally small. In the case of collapsing dust, there are certain initial configurations in which the collapse leads to the formation of a naked singularity.

Scattering of scalar fields by spherical gravitational collapse

We study the scattering of a scalar field, massive or massless, by a collapsing spherical star. The main point of interest is the infinite Doppler effect measured by an observer, at rest in Schwarzschild coordinates. We construct the functional framework associated with this phenomenon, and we prove the existence and strong asymptotic completeness of the wave operators describing the scattering of the field by the space-time curvature and the asymptotically characteristic moving boundary of the star.

Can spherical gravitational collapse in Newtonian theory be prevented by non-radial stresses?

A solution of the Newtonian equations of continuous media is presented in which the radial stresses vanish everywhere inside a spherical distribution of matter at rest. The distribution remains at rest under the influence of tangential stresses only. These stresses are the «classical limit» of the tangential stresses of the corresponding system in general relativity.

Thermodynamics of a model of nonadiabatic spherical gravitational collapse

In this work, a thermodynamic treatment of a Friedmann-like model of nonadiabatic spherical gravitational collapse is presented. The calculations have been performed according to Eckart's theory of dissipative relativistic fluids, while the diffusion approximation has been adopted for the radiation transport. The conclusions deduced are in agreement with the predictions of the theory of late stellar evolution.

Gravitational Collapse of an Isothermal Sphere

view Abstract Citations (294) References (31) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gravitational Collapse of an Isothermal Sphere Foster, Prudence N. ; Chevalier, Roger A. Abstract We investigate the spherical gravitational collapse of isothermal spheres using numerical hydrodynamics. The initial configuration is close to hydrostatic equilibrium. If the initial density profile has a finite core radius (i.e., it is not singular), supersonic velocities develop during the initial collapse. At the time of central core formation, when the central density diverges, the central inflow velocity approaches -3.3 times the sound speed and the central density approaches an r-2 profile. These conditions are similar to those found in the self-similar solution of Larson and Penston, but occur only at the center and not at all radii as in the selfsimilar solution at core formation. For the marginally stable equilibrium isothermal sphere, with an initial outer cloud radius to core radius ratio of 3.2, the central mass accretion rate steadily declines after core formation. Only if this ratio is ≳20 does the collapse enter a constant mass accretion rate, as occurs in the self-similar solutions developed by Shu. Assuming optical transparency, we calculate line profiles for the computed collapse. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173236 Bibcode: 1993ApJ...416..303F Keywords: STARS: PRE-MAIN-SEQUENCE; HYDRODYNAMICS; STARS: FORMATION full text sources ADS | data products SIMBAD (3)

An analytic model of radiating spherical gravitational collapse

The gravitational collapse of a radiating sphere consisting of a heat-conducting fluid with shear-free and radial motion is considered. In the exterior of the sphere we assume Vaidya's outgoing metric, while in the interior we have a neutrino flux described by a pure radiation term in the energy-momentum tensor. At first, a brief review including some new considerations of a similar, previously studied model, is given. Then, a new model is presented, in which the space-time interior to the collapsing sphere is conformally flat.

Precursory singularities in spherical gravitational collapse.

General conditions are developed for the formation of naked precursory (``shell-focusing'') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.

Spherical gravitational collapse with photon emission and a generalized Schwarzchild interior solution

The general dynamical equations for perfect fluid filled spheres with an outward flux of photons are derived. The vital role played by the energy density of the free gravitational field in accelerating photon production has been emphasized. It is pointed out that even when the material energy density is finite, the energy density of the free gravitational field can take infinitely large values resulting in vanishing surface area of the star. A generalized Schwarzschild interior solution with conformally flat geometry but with photon emission has been obtained. It is pointed out that the interior conformal coordinate system bears a strong resemblance to the exterior Krushkal coordinates. It is shown that for spherical star the invariant velocity of the fluid particles, falling towards the centre, is proportional to its radius suggesting that the outer envelopes collapse at a faster rate than the core part. It is shown that the interior radiating solution can be matched with generalized Schwarzchild exterior solution.

Structure of singularities in the spherical gravitational collapse of a charged null fluid.

Structure of singularities in the spherical gravitational collapse of a charged null fluid.

Computations of spherical gravitational collapse using null slicing

Results are presented from a numerical study of spherical GR gravitational collapse using 'observer-time' null slicing. Data on the initial null slice are generated by computing collapse from an initial spacelike slice by means of a standard method and noting parameter values at successive grid points as they are passed by a hypothetical null ray propagating out from the centre. Collapse is then followed to black hole formation using the observer-time code.

Comment on "Naked singularities in self-similar spherical gravitational collapse"

Comment on "Naked singularities in self-similar spherical gravitational collapse"

Self-similar spherical gravitational collapse and the cosmic censorship hypothesis

We show that a self-similar general relativistic spherical collapse of a perfect fluid with an adiabatic equation of statep=(γ−1)ϱ and low enough γ values, results in a naked singularity. The singularity is tangent to an event horizon which surrounds a massive singularity and the redshift along a null geodesic from the singularity to an external observer is infinite. We believe that this is the most serious counter example to cosmic censorship obtained so far.

Naked singularities in self-similar spherical gravitational collapse.

We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (\ensuremath{\Gamma}-1\ensuremath{\ll}1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold.

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.

THE GRAVITATIONAL COLLAPSE OF A HIGGS SCALAR FIELD

We investigate the spherical gravitational collapse of a Higgs scalar field in the frame-work of numerical relativity. This problem is stimulated by the inflationary universe scenario.It is supposed that a sufficient fluctuation of the Higgs scalar field at the supercooled expan-sion stage causes gravitational collapse. We use an imitative model to give some estimate ofblack-hole formation at the reheating time. In order to form a black hole from a fluctuationwith a size of the same order as the cosmological horizon, the scalar field of the fluctuationmust evolve with a time delay of about one expansion time relative to its surroundings andthe mass of the black hole formed is of order 10 4 g.