Conformally equivalent metrics in bimetric general relativity

Space-times conformal to physical space-time are considered, assuming the nongravitational energy is conservative after the conformal transformation. Necessary and sufficient conditions satisfied by the conformal factor axe found for a given type of transformation of the energy tensor. The weak gravitational field is defined and the coordinate conditions for the existence of conformal factors in such a field are obtained.     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

A comparative analysis of the adiabatic stability of anisotropic spherically symmetric solutions in general relativity

A family of static solutions of the Einstein field equations with spherical symmetry for a locally anisotropic fluid with homogeneous energy density is obtained. These solutions depend on two adjustable parameters related to degree of anisotropy of the fluid. Some known solutions may be recovered for specific values of these parameters. As a difference to other known solutions it is possible to change the grade of anisotropy of the model, keeping the same functional dependence on the coordinates. By means of a slow adiabatic contraction, the stability of the obtained solutions is studied. Also, it is shown, how it is possible to enhance the stability of the models by adjusting the parameters, and to obtain more compact configurations than those obtained with other similar anisotropic solutions, while the dominant or strong energy condition holds within the sphere.     

Magnetized cylindrically symmetric universe in general relativity

A magnetized cylindrically symmetric universe with two degrees of freedom in which the free gravitational field is Petrov type I degenerate, is obtained. The magnetic field is due to an electric current produced along the x-axis. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. The behaviour of the model when magnetic field tends to zero and other physical aspects of the model are also discussed.     

Spherically symmetric solutions in five-dimensional general relativity

The most general time-independent spherically symmetric (in the usual three space dimensions) solution to the five-dimensional vacuum Einstein equations is found, subject to the existence of a Killing vector in the fifth direction. The significance of these solutions is discussed within the context of a previously proposed extension of the Kaluza-Klein model in which the universe, although (4+1)-dimensional, has evolved over cosmic times into an effectively (3+l)-dimensional one.     

Static spherically symmetric solutions in general projective relativity

Static spherically symmetric solutions have been obtained for general projective relativity withn=0 andn0 both in isotropic and curvature coordinates. In curvature coordinates, only a restricted exact solution is possible. However, an approximate solution can always be obtained following a method similar to Vanden Bergh. In these spacetimes there is no horizon, but only a naked singularity atr=0. Thus there are no black holes. It is shown that there is no solution in static, spherically symmetric, conformally flat spacetime.     

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 stationary axially symmetric interior solutions in general relativity

This note presents the coordinate transformation by which the coordinate condition of a previous paper (Rawson-Harris, 1972) may be imposed.     

Spherically symmetric solutions with heat flow in general relativity

Some new solutions of shear-free imperfect fluid spheres with heat flux in the radial direction are obtained. They have isotropic pressure and could be the generalizations of earlier solutions of Nariai and of Banerjee and Banerji for perfect fluid without dissipation.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Conformally symmetric semi-Riemannian manifolds

In this paper we introduce the concept of conformal curvature-like tensor on a semi-Riemannian manifold, which is weaker than the notion of conformal curvature tensor defined on a Riemannian manifold. By such kind of conformal curvature-like tensor we give a complete classification of conformally symmetric semi-Riemannian manifolds with generalized non-null stress energy tensor.     

Cylindrically symmetric Zel'dovich fluid distributions in general theory of relativity

The problem of charged perfect fluid distribution is investigated when the space-time is described by the Einstein-Rosen metric. It is shown that with assumed cylindrical symmetry the cosmological constant vanishes, the electromagnetic field becomes source-free, and the perfect fluid reduces to Zel'dovich fluid withp=. Sets of exact solutions for this case have been obtained and the corresponding solutions for Brans-Dicke-Maxwell fields have been derived. For these solutions the Einstein-Rosen metric, however, goes over to three-parameter Marder metric in Brans-Dicke theory.     

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of(N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity(TEGR).The fundamental gravitational field variables are the(N+1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution(Schwarzschild(4+1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.     

An anisotropic magnetized viscous fluid cosmological model in general relativity

We investigate the behavior of a magnetic field in a viscous fluid cosmological model where the free gravitational field is of Petrov type D and the coefficient of shear viscosity is proportional to the rate of expansion in the model. Also discussed are the behavior of the model when the magnetic field tends to zero and some other physical properties.     

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.     

Non-static spherically symmetric clusters of particles in general relativity: I

In an ingenious way rotation (but no angular momentum) has been introduced in the case of spherical symmetry by Einstein, who has considered a stationary cluster of particles moving freely under the influence of the gravitational field produced by all of them together. The aim of the present work is to extend his idea to the non-static case, and it seems that under some circumstances instead of an indefinite gravitational collapse there is a minimum of the volume and a bouncing back.     

The energy distribution for a spherically symmetric isolated system in general relativity

The problems of the tolal energy and quasilocalenergy density or an isolated spherically symmetric static system in general relativity (GR) are considered with examples of some exact suintions. The field formulation of GR dereloped earlier hy L. P. Grishchuk. el al. (1984). in ihe framework of which all the dynamical fields, including the gravitation field, are considered in a fixed background spacetime is used intensively. The exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York. Jr. (1993) as well as discussed with respect to the principle of nonlocalization of the gravitational energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the field configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which are difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.     

The general class of the vacuum spherically symmetric equations of the general relativity theory

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g ₀₀ and g ₂₂ is obtained. The properties of the found solutions are analyzed.