Static charged dust in general relativity

Solutions of the Einstein-Maxwell equations for static charged dust are discussed. Contrary to what has been asserted earlier it is found that cylindrically symmetric and plane symmetric solutions with the following properties, exist: (a) They are regular in the interior region; (b) the mass density is positive and vanishes at the boundary; (c) the metric, its first derivate, and the electrical field strength are continuous at the boundary; (d) the solutions are mirror symmetric in the plane symmetric case.     

Non-existence of stationary,axially symmetric,asymptotically flat solutions of the Einstein equations for dust

It is shown that the Einstein equations for stationary, axially symmetric distributions of dust do not admit regular, asymptotically flat solutions, provided the mass density is strictly positive everywhere.     

General relativity in a (2 + 1)-dimensional space-time

General relativity is formulated for a (2+1)-dimensional space-time. Solutions to the vacuum field equations are locally flat. There are no gravitational waves and no Newtonian attraction between masses. The geometry around a point mass is a cone (locally flat) where the angle deficit at the apex is proportional to the mass. A uniform density planet has a spherical cap interior and a conical exterior solution. A convex polyhedron represents a closed universe with point masses at its vertices and approximates a static spherical universe of uniform density dust.     

A Weyl-Dirac geometric particle

A spherically symmetric entity with the Weyl-Dirac geometry holding in its interior is investigated. The structure is determined by the presence of the Dirac gauge function, which creates a mass density. Two models are obtained, one that can describe a cosmic body, the other an elementary particle.Deceased December 18, 1995.     

Collapse and rebound of a charged dust-like star

It is shown that a charged spherically symmetric star, made out of a continuous superposition of thin shells with Poincaré stresses, undergoes gravitational collapse in free fall like an uncharged star of dust. The interior solution is a Friedmann universe matching the Reissner-Nordström geometry at the boundary of the star. When the absolute value of the chargeQ does not exceed the massM, the star rebounds elastically inside the event horizon at the radial coordinateQ ²/(2M). The further history of the charged star after the bounce is analyzed. Besides, a simple mechanism which accounts for the development of Poincaré stresses in an originally charged star of dust is suggested. It is also verified that the energy density is nonnegative all along the collapse process.     

A class of static charged dust spheres in general relativity

Using static spherically symmetric space-times with associated 3-spaces obtained as hypersurfacest= const as 3-spheroidal, a class of physically viable relativistic models for spherical distributions of uniformly charged dust in equilibrium is obtained. The charged analog of Schwarzschild interior solution given by Cooperstock and de la Cruz follows as a particular case of this class.     

Brane-world stars from minimal geometric deformation, and black holes

Using the effective four-dimensional Einstein field equations, we build analytical models of spherically symmetric stars in the brane-world, in which the external space-time contains both an ADM mass and a tidal charge. In order to determine the interior geometry, we apply the principle of minimal geometric deformation, which allows one to map general relativistic solutions to solutions of the effective four-dimensional brane-world equations. We further restrict our analysis to stars with a radius linearly related to the total general relativistic mass, and obtain a general relation between the latter, the brane-world ADM mass and the tidal charge. In these models, the value of the star’s radius can then be taken to zero smoothly, thus obtaining brane-world black hole metrics with a tidal charge solely determined by the mass of the source and the brane tension. We find configurations which entail a partial screening of the gravitational mass, and general conclusions regarding the minimum mass for semiclassical black holes are also drawn.     

Gravitational collapse in free fall of a slowly rotating star

The Oppenheimer-Snyder model of a spherically symmetric collapse in free fall is generalized to the case in which the star possesses a small rotation. The exterior geometry is chosen to be the Kerr metric in synchronous coordinates, discarding terms of the order (a/r)². The interior geometry is constructed by adding to the exact metric of the nonrotating case an off-diagonal first-order term in the parametera. This term is determined in part by requiring the validity of the junction conditions at the star's surface and, also, by demanding the conserved angular momentum of the source be equal toMa, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid (dust) nonuniformly rotating relative to the synchronous frame, which is no longer comoving with the stellar matter. The dynamics of collapse is qualitatively the same as in the spherically symmetric case. Again the star's surface crosses the event horizon when the mass density is finite everywhere, and space-time has not developed any singularity as viewed by freely falling observers at rest in the synchronous frame.Based on a dissertation submitted (by J. C. F.) to the Facultad de Ciencias Fisicas y Matemáticas, Universidad de Chile. in partial fulfilment of the requirements of the Magister degree.     

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.Supported in part by The National Science Foundation under Grant No. INT 782-5663.Supported in part by Consejo Nacional de Investigaciones Cientificas y Technologicas (CONICIT), Venezuela.     

Axially symmetric,uniformly rotating neutron stars in general relativity: a non-perturbative approach

The equilibrium problem for an axially symmetric, uniformly rotating, elastic solid neutron star is considered within the framework of a new formulation of relativistic elasticity. The analysis is fully relativistic and free of any assumption about the existence of a globally relaxed state of the star. Static configurations may exist only for rigid motions, and for such motions a set of six Einstein equations for six variables is proposed. Due both to the importance of elastic-solid lattices for the structure of neutron stars crusts and to the lack, up to now, of satisfactory axially symmetric perfect fluid interior solutions matching an asimpotically flat exterior, the results seem to indicate the possibility of constructing physically valid models of axially symmetric astrophysical objects in general relativity. The particular case of non-rotating axially symmetric elastic sources is also discussed.     

Anisotropic relativistic stellar models

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.     

Dynamics of charged plane symmetric gravitational collapse

In this paper, we study dynamics of the charged plane symmetric gravitational collapse. For this purpose, we discuss non-adiabatic flow of a viscous fluid and deduce the results for adiabatic case. The Einstein and Maxwell field equations are formulated for general plane symmetric spacetime in the interior. Junction conditions between the interior and exterior regions are derived. For the non-adiabatic case, the exterior is taken as plane symmetric charged Vaidya spacetime while for the adiabatic case, it is described charged plane symmetric spacetime. Using Misner and Sharp formalism, we obtain dynamical equations to investigate the effects of different forces over the rate of collapse. In non-adiabatic case, a dynamical equation is joined with transport equation of heat flux. Finally, a relation between the Weyl tensor and energy density is found.     

Rotationally Symmetric Massless Modes in Closed Robertson-Walker Universe

The aim of the present paper is to investigate the minimally coupled rotationally symmetric scalar field configurations in spatially closed Friedman-Robertson-Walker Universe with incoherent dust. We have got the closed form solution of the Klein-Gordon equation in terms of two real-valued linearly independent hypergeometric functions. The orthonormal set of positive-frequency-like parity modes thereafter derived points out that each parity given state is conformally built up of three Einsteinian particle states and also leads to the explicit coordinate-representation of the field propagator.     

Shapes of nuclear configurations in a cranked harmonic oscillator model

The shapes of nuclear configurations are calculated using Slater determinants built with cranked harmonic oscillator single particle states. The nuclear forces role is played by a volume conservation condition (of the potential or of the density) in a first part. In a second part, we have used the finite range, density dependent interaction of Gogny. A very simple classification of configurations emerges in the first part, the relevant parameter being the equatorial eccentricity of the nuclear density. A critical equatorial eccentricity is obtained which governs the accession to the case for which the nucleus is oblate and symmetric around its axis of rotation. Nuclear configurations calculated in the second part observe remarkably well these behaviours.     

Quantization of the Interior Schwarzschild Black Hole

We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.     

Molecular Dynamics Simulation of Icosahedral Transformations in Solid Cu-Co Clusters

We study the icosahedral transformations of solid Cu Co clusters with different initial configurations by using molecular dynamics with the embedded atom method. It is found that the formation of symmetric icosahedral cluster is strongly related to the atomic number and initial configuration. The transformation originates from the surface into the interior of the cluster and is a structural change which is rapid and diffusionless. The icosahedral clusters with any composition and configuration, such as core-shell or three-shell duster, can be prepared by the means of solid-solid phase transition in bimetallic clusters.     

The Newtonian analogue of the relativistic Oppenheimer-Snyder solution

The gravitational collapse of a spherically symmetric mass of incoherent matter (dust) is investigated within the framework of the Newtonian theory and it is shown that the results are identical to the relativistic results obtained by Oppenheimer and Snyder.     

尘埃粒子的时空结构及其性质

讨论了尘埃粒子解的时空结构及其性质，导出了尘埃粒子的内空间的离散结构.证明了尘埃粒子内部的物质球是一个无坐标的平直球，因而具有最小的体积和整体的关联性.导出了在尘埃粒子的内外时空中的径向测地线并说明其连续性.阐述了由这个解所揭示的物质、引力与时空之间的内在联系. 关键词： 尘埃粒子 离散时空 测地线     

Streaming instability of a dusty plasma in the presence of mass and charge variation

We study the effect of the mass and charge dynamics on the collective behaviour of a dusty plasma. It is shown that the finite non-zero streaming velocity of the dust grains leads to a novel coupling of the dust mass fluctuation with other dynamic variables of the plasma and the grains. The mass fluctuations causes a collisionless dissipation and provides an alternate channel for the beam mode instability to occur. Physically the negative energy wave associated with the beam mode couples to the mass fluctuation induced dissipative medium to produce the instability. We conclude that the higher value of the ion mass density to the dust mass density ratio reduces the threshold value for the onset of the instability. Its application in the astrophysical context is discussed.     

Stability of small planar dust cluster in the presence of an external magnetic field

Oscillations and stability of planar symmetric dust clusters shaped as a regular polygon and a regular polygon with a particle at the center in the presence of an external uniform magnetic field are analyzed. The structure stability against small perturbations is considered. To this end, the equation of motion was linearized with respect to small coordinate variations. As a result, a dispersion relation (quartic algebraic equation) was derived and numerically studied for particular types of interactions between particles. A comparison of stability regions for a quadrangle and a triangle with a particle at the center, as well as a pentagon and a quadrangle with a particle at the center shows that there are ranges of parameters, where configurations without particle at the center are stable and configurations with a particle at the center are unstable, and vice versa.