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.     

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.     

The rate of growth of the magnetic energy density during a gravitational collapse

It is shown that during an isotropic gravitational collapse of a fluid with infinite electrical conductivity, the magnetic energy density cannot grow faster than ^4/3 no matter the equation of state, where is the total proper energy density. If the equation of state is=c ², where 01, then the rate of growth of the magnetic energy density in such a collapse is proportional to ^4/3(1+). If an isotropic collapse is also locally adiabatic, it is shown, independently of any equation of state, that the rate of increase of the magnetic energy density is proportional tor ^4/3, wherer is the proper material density. If the collapse is nonisotropic, shear can modify these results. Numerical estimates of the magnetic field strength at various stages in the collapse of a magnetic star are given.     

Role of initial data in higher dimensional quasi-spherical gravitational collapse

We study the gravitational collapse in (n+2)-D quasi-spherical Szekeres space–times (which possess no Killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate r as the initial value for the scale factor R, we consider a power function of r as the initial scale for the radius R. We examine the influence of initial data on the formation of singularity in gravitational collapse.     

Radiating fluid distribution interacting with scalar field

Taking the combined energy-momentum tensor for a perfect fluid, radially expanding the radiation and zero-mass scalar field, we investigate their interaction and obtain five new analytic solutions in a spherically symmetric Einstein universe. For the corresponding models various physical and geometrical properties are discussed. In one case an interesting equation of state is derived.     

Luminescence of statically annihilating centers with an inhomogeneous distribution

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 53, No. 3, pp. 380–386, September, 1990.     

Force distribution in an inhomogeneous sandpile

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre. Received 29 January 1998 and Received in final form 7 September 1998     

Computation of demagnetizing fields and particle distribution in magnetic fluid with inhomogeneous density

A new algorithm for calculating magnetic fields in a concentrated magnetic fluid with inhomogeneous density is proposed. Inhomogeneity of the fluid is caused by magnetophoresis. In this case, the diffusion and magnetostatic parts of the problem are tightly linked together and are solved jointly. The dynamic diffusion equation is solved by the finite volume method and, to calculate the magnetic field inside the fluid, an iterative process is performed in parallel. The solution to the problem is sought in Cartesian coordinates, and the computational domain is decomposed into rectangular elements. This technique eliminates the need to solve the related boundary-value problem for magnetic fields, accelerates computations and eliminates the error caused by the finite sizes of the outer region. Formulas describing the contribution of the rectangular element to the field intensity in the case of a plane problem are given. Magnetic and concentration fields inside the magnetic fluid filling a rectangular cavity generated under the action of the uniform external filed are calculated.     

Kinetic energy of an inhomogeneous electron gas

It is well known that the kinetic energy of a system of N noninteracting particles in an external field V(r) in the nondegenerate ground state is a universal functional of the particle density (r) [1]. However, the explicit form of this functional is defined only for a certain class of functions (r). In particular, in the case of an almost constant or a slowly varying density we obtain the wellknown Thomas-Fermi-Weizsäcker-Kirzhnits functional [1, 2]. In [3] the kinetic energy functional of an electron in an atom is obtained in the WKB approximation. The kinetic energy of electrons with quantum numbers n andl is represented as the sum of two terms. The first term is written in the form of the density of the electrons with the given quantum numbers times some orthogonalized pseudopotential, which takes into account the orthogonality of their wave functions with respect to the core (its form is discussed below). The second term is the intrinsic kinetic energy of the electrons. The introduction of an orthogonalized pseudopotential is very convenient for the calculation of atomic properties [4, 5]. It is therefore of great interest to extend the results of [3] to the case of an electron gas in a metal and to obtain an expression for its orthogonalized crystalline pseudopotential. The solution of these problems is the aim of the present paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 117–120, July, 1977.     

Elastic energy of an inhomogeneous solid solution. III. Quasiperiodic distribution of the particles

The elastic interaction potential for bcc and fcc crystals is determined in a microscopic approximation. The conditions for the formation of a quasiperiodic structure are determined in their dependence on the elastic moduli.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 75–79, January, 1981.We are grateful to the students A. Bilas, A. Merkulin, S. Laptev, and S. Soldatov for assistance in calculating the coefficients b (n).     

Exchange energy density of inhomogeneous electron gas near a metal surface

Using the first-order density matrix of an infinite barrier model of a metal surface, the exchange energy density can be evaluated exactly as a function of the distance z from the barrier. This result is compared with the local approximation $\text{?}\text{3}\text{4}\text{e}{}^2\text{(}\text{3}\text{π}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{[?(z)]}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ where the electron density in the model. The local approximation follows the exact result quite closely at all z but leads to a large percentual error in the integrated surface exchange energy.     

On the nonsymmetric,gravitational collapse of an infinite,dust-filled cylinder

Nonsymmetric terms or angle-dependent terms in the power series expansion of Einstein's equations are considered. It is shown, first, that they do not influence the time evolution of the symmetric terms and, second, that they do not remain bounded as the cylinder collapses. However, the major contribution to the density arising from the symmetric terms makes the nonsymmetric contribution progressively more insignificant as the collapse proceeds.     

Absorption of ultrashort electromagnetic pulses in plasma with inhomogeneous distribution of density and temperature

The analysis of influence of the inhomogeneous distribution of temperature and density of atoms on the probability of absorption of ultrashort electromagnetic pulses in plasma is carried out. A specific example of divertor plasma of tokamaks and absorption in the Lyman series (at the Ly-α line) is considered. It is shown that the absorption probability may exceed relative populations of excited levels in divertor plasma by several orders of magnitude. The influence of the pulse duration on the probability of excitation of an atomic level is considered. The results suggest a possibility of a sharp increase in a fluorescence signal under the action of an ultrashort pulse.     

A gravitational collapse singularity theorem consistent with black hole evaporation

Letters in Mathematical Physics - The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole...     

Parton energy loss in an inhomogeneous color medium

The contribution of stochastic inhomogeneities to the parton collisional loss in a color medium is considered.     

Genericity and stability of naked singularities arising in an inhomogeneous dust collapse

In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate r. We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense.     

Gravitational collapse with decaying vacuum energy

The effect of dark energy on the end state of spherical radiation collapse is considered within the context of the cosmic censorship hypothesis. It is found that it is possible to have both black holes as well as naked singularities.