Shear-free spherically symmetric perfect fluid solutions with conformal symmetry

In 1987, Dyer, McVittie and Oattes determined the general relativistic field equations for a shear-free perfect fluid with spherical symmetry and a conformal Killing vector in thet-r plane, which depend on an arbitrary constantm. Two particular solutions of these equations were given recently by Maharaj, Leach and Maartens, as well as a partial solution thought to be valid for almost allm. In this paper, this solution is completed for four values ofm, and it is shown that it cannot be completed for any others by currently available techniques; however, a new solution of a different form, but also depending on a Weierstrass elliptic function, is found for a further value ofm. None of these metrics are conformally flat; one of them has a constant expansion rate.     

A general integral of the Jordan-Brans-Dicke field equations for static spherically symmetric perfect fluid distributions

The Jordan-Brans-Dicke field equations [1] contain the four-dimensional field equations of the five-dimensional projective unified theory. As it should be, Einstein's theory is incorporated as a limiting case. In this paper we present a method to determine explicitly for every static spherically symmetric solution of Einstein's theory with perfect fluid an analogous solution of Jordan-Brans-Dicke theory. As a particular example a “generalized interior Schwarzschild solution” is given.     

A class of spherically symmetric ideal fluid fields

It is shown that the equation of state =p for an ideal fluid follows from the condition of integrability of Einstein's equations for the metric ds²=R²T²d²+e²dr²–e²dt². In this case, the system of Einstein's equations turns out to be indeterminate and has an infinite number of solutions for R 0. These solutions describe fields with nonzero acceleration, expansion, and shear tensor of particles. The obtained solutions correct the results obtained by J. Hajj-Boutros, J. Math. Phys.,26, 771 (1985). The unique solution of Einstein's equations for the state =p of a fluid is obtained to within arbitrary constants for R=0.Naval Engineering College, Novosibirsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 91–94, June, 1992.     

Physical properties of Buchdahl's three-parameter static spherically symmetric perfect fluid metrics

The physical properties of a static spherically symmetric perfect fluid metric proposed by Buchdahl are investigated. The general solution can be written in terms of associated Legendre functions. If the adiabatic sound speed is to be less than the velocity of light at the boundary of the sphere, its radius will be larger than 1.238 times the Schwarzschild radius. Two particular solutions are studied in detail.     

Spherically symmetric charged perfect fluid distributions executing shear-free motion

A method to obtain exact solutions characterizing spherically symmetric charged perfect fluid distributions undergoing shear-free motion has been discussed. This method makes use of the criterion that the solution be free from movable critical points as has been employed earlier by Shah and Vaidya. Two solutions have been obtained, one of which is new and the other is the recent solution due to Sussman.     

Viscous fluid in static spherically symmetric space-time

The paper presents a static spherically symmetric viscous fluid solution of Einstein field equation, assuming an equation of statep=(γ?1)ρ. Though static, the solution has expansion, shear, and acceleration and can explain cosmological red shift. Also it has a particle horizon. The singularity at the origin and larger viscosity make it unfit to represent a real universe.     

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

In this paper, we classify static spherically symmetric (SS) perfect fluid space-times via conformal vector fields (CVFs) in f(T) gravity. For this analysis, we first explore static SS solutions by solving the Einstein field equations in f(T) gravity. Secondly, we implement a direct integration technique to classify the resulting solutions. During the classification, there arose 20 cases. Studying each case thoroughly, we came to know that in three cases the space-times under consideration admit proper CVFs in f(T) gravity. In one case, the space-time admits proper homothetic vector fields, whereas in the remaining 16 cases either the space-times become conformally flat or they admit Killing vector fields.     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.     

Some cylindrical symmetric nonstatic perfect fluid distributions in general relativity with pressure equal to density

In this paper we have derived some models of cylindrical symmetry in which source of gravitational field is perfect fluid with pressure equal to energy density.     

On spherically symmetric fields in gauge theories

Gauge fields admitting spherical symmetry are listed. Spherically symmetric solutions of Yang-Mills equations and spherically symmetric magnetic monopoles are studied. A simple exact solution of the Yang-Mills and Einstein equations is found.     

A class of spherically symmetric solutions with conformal killing vectors

Spherically symmetric solutions with a conformal Killing vector in the (r, t) surface allow the null geodesics to be found with relative ease. Knowledge of the null geodesics is essential to calculating the optical properties of a solution via the optical scalar equations. Solutions of this type may be useful for the treatment of the optical properties of an inhomogeneous universe. We first address the question of whether the large class of spherically symmetric solutions found by McVittie possess conformal symmetry. We also investigate the potential for using conformal Killing vectors to aid in the solution of Einstein's Field Equations.     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

On spherically symmetric singularity-free models in relativistic cosmology

The introduction of time dependence through a scale factor in a non-conformally flat static cosmological model whose spacetime can be embedded in a five demensional flat spacetime is shown to give rise to two spherical models of universe filled with perfect fluid acompannied with radial heat flux without any Big Bang type singularity. The first model describes an ever existing universe which witnesses a transition from state of contraction to that of ever expansion. The second model represents a universe oscillating between two regular states.     

On Datta's spherically symmetric systems in general relativity

The problem tackled by B. K. Datta, [1] in a recent paper concerning non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case. A full classification of the possible motions is given.The author wishes to express his thanks to Professor C. W. Kilmister for helpful discussions.     

On spherically symmetric Finsler metrics of scalar curvature

Spherically symmetric Finsler metrics form a rich class of Finsler metrics. In this paper we find equations that characterize spherically symmetric Finsler metrics of scalar flag curvature. By using these equations, we construct infinitely many non-projectively flat spherically symmetric Finsler metrics of scalar curvature.     

Static spherically symmetric anisotropic fluid distribution in presence of electromagnetic field

Einstein’s field equations of general relativity corresponding to the anisotropic (principal stresses unequal) static fluid sphere in presence of electromagnetic field have been solved exactly. The integration constants are determined by matching the obtained solution with the Reissner-Nordström solution over the boundary. It has been found that the flaid model has non-negative expression for mass density and pressure. The mass density and stresses are everywhere regular and monotonically decreasing functions of the radial coordinate.     

Axially symmetric rotating body consisting of a perfect fluid

An alternative method of obtaining the equilibrium configurations of a rotating body consisting of a perfect fluid is outlined. Basically, the method involves recasting the gravitational hydrodynamic equations into a set of partial differential equations of first order in the radial direction such that a center-outward integration can be performed. Specifically, with suitable initial conditions at the origin of anr, grid, a numerical integration is performed outward along a number of selected-rays, with the required derivatives at each step being determined numerically from the values of the functions on the different rays. Applicable to both Newtonian and relativistic formulations, the technique is similar to that often used to obtain equilibrium configurations in spherically symmetric models.     

A one-parameter family of cylindrically symmetric perfect fluid cosmologies

Non-stationary cylindrically symmetric one-parameter solutions to Einstein's equations are given for a perfect fluid. There is a time singularity (t=0) at which the pressurep and density are equal to + throughout the radial coordinate range 0 r < , but the solutions are well behaved fort > 0,p and decreasing steadily to zero asr increases through the range 0r<, or as t increases through the range 0<t<. The motion is irrotational with shear, expansion and acceleration. The family of solutions, of Petrov type I, are generally spatially inhomogeneous, of class B(ii), having two spacelike Killing vectors which are mutually orthogonal and hypersurface orthogonal, associated with an orthogonally transitive groupG ₂. The particular members for which there are equations of statep=/3 andp= are specially considered.