Cosmological models in general relativity

LRS Bianchi type-I space-time filled with perfect fluid is considered here with deceleration parameter as variable. The metric potentialsA andB are functions of x as well as t. Assuming B′/B = f (x), where prime denotes differentiation with respect to x, it was found thatA = (l′/l)B andB = lS(t), wherel = f (x) andS is the scale factor which is a function of t only. The value of Hubble’s constantH ₀ was found to be less than half for non-flat model and is equal to 1.3 for a flat model     

Cosmological shock waves in general relativity

The problem of finding spherically symmetric self-similar solutions of Einstein's field equations with a barotropic perfect fluid, which can be joined through a shock wave to some cosmological models, is considered. It is found that such solutions comprise an expanding shell of matter surrounding a horizon with an interior singularity.     

Charged spinning fluids in general relativity

The treatment of neutral spinning fluids in general relativity due to Ray and Smalley is generalized, by considering the fluid as charged and having a magnetic dipole moment proportional to the spin.     

Neutral perfect fluids of Majumdar-type in general relativity

We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations proposed by Ida to include charged perfect fluid sources. We impose the equation of state ρ+3p = 0 and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges Q and −Q. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.     

Cosmological special relativity

Recently we presented a new special relativity theory for cosmology in which it was assumed that gravitation can be neglected and thus the bubble constant can be taken as a constant. The theory was presented in a six-dimensional hvperspace. three for the ordinary space and three for the velocities. In this paper we reduce our hyperspace to four dimensions by assuming that the three-dimensional space expands only radially, thus one is left with the three dimensions of ordinary space and one dimension of the radial velocity.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) vector fields(pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

Cosmological models in general relativity and brans-dicke theories: a comparison

We review general relativistic and Brans-Dicke cosmological models of the early universe and for the present phase. Both theories render similar results, in general, as far as Mach's principle is concerned. There is some difference in the stability problem for the inflationary phase, and we point out how to test one theory against the other experimentally.     

Homogeneous and hypersurface-homogeneous shear-free perfect fluids in general relativity

Shear-free, general-relativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurface-homogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density and the presurep of the fluid are related by a barotropic equation of statep = p(), where +p 0. Under such circumstances, it follows that either the fluid's volume expansion rate or the fluid's vorticity (i.e., rotation) must vanish. In the homogeneous case, this leads to only two possibilities: either = = 0 (the Einstein static solution), or 0, = 0 (the Gödel solution). In the hypersurface-homogeneous case, the situation is more complicated: either = 0, 0 (as exemplified,inter alia, by the Friedmann-Robertson-Walker models), or 0, = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or = = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.     

Cosmological solutions foe a spinor field in the general theory of relativity

We consider models of the universe containing linear and nonlinear spinor matter. It is assumed that the linear spinor matter is described by the generally covariant Dirac equation, and the nonlinear by the generally covariant Ivanenko-Heisenberg equation.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 68–71, December, 1973.     

On the quantization of general relativity in anholonomic variables

In discussing Bohr-Sommerfeld-like quantum rules for gravity, it is argued that Einstein's Riemannian theory of general relativity rather leads to a quantum field-mechanics than to a quantum-field theory of gravity. We construct the canonically conjugate coordinates and momenta of this gravito-dynamics in the framework of the Einstein-Cartan teleparallelism.     

Cosmological relativity: A special relativity for cosmology

Under the assumption that Hubble's constant H₀ is constant in cosmic time, there is an analogy between the equation of propagation of light and that of expansion of the universe. Using this analogy, and assuming that the laws of physics are the same at all cosmic times, a new special relativity, a cosmological relativity, is developed. As a result, a transformation is obtained that relates physical quantities at different cosmic times. In a one-dimensional motion, the new transformation is given by

Numerical determination of time transfer in general relativity

This paper determines the travel time of a light ray connecting two points in the space-time solving numerically a two-point boundary value problem by means of the shooting method. For the resolution of this problem multiple precision floating-point arithmetic is required. We have studied distinct implementations of the shooting method attending to the way in which the Jacobian appearing at each iteration is approximated. We have shown that by using Magnus expansions to solve the differential equation for the Jacobian, one obtains a better efficiency of the shooting method. Also, a comparison between the numerical results obtained through the application of the shooting method and those derived by Le Poncin-Lafitte et al. (Class Quantum Grav, 21:4463-4483, 2004) from perturbative expansions of the world function is made.     

On the spherical symmetry of static perfect fluids in general relativity

We present a theorem which establishes uniqueness, in particular spherical symmetry, of a wide class of general relativistic, static perfect-fluid models provided there exists a spherically symmetric model with the same equation of state and surface potential. The method of proof, which is inspired by recent work of Masood-ul-Alam, is illustrated by demonstrating uniqueness of a class of solutions due to Buchdahl which correspond to an extreme case of the inequality on the equation of state required by our theorem.     

Description of spinning particle in general relativity using commuting spin variables

A general relativistic extension of a recently proposed model of spinning particle using commuting spin variables is given. The results found earlier in an approach using anticommuting (Grassmannian) variables are reproduced and extended to the case with nonzero torsion. The quantization of the model is performed via Feynman path integral and a discretization procedure is proposed leading to a covariant second-order differential equation for the propagator which in the case with zero torsion can be reduced to general relativistic Dirac equation with δ-function source.     

On the measure of proper time in general relativity

The theoretical measure of proper time on a moving particle in general relativity is the aggregate of infinitesimal clock readings in successive inertial frames along its space-time path. This raises the question of whether the proper time can be satisfactorily measured by a clock permanently located with the particle. An investigation is made of the likely effects of acceleration, or equivalently of a gravitational field, on atomic, nuclear, and particle clocks. The orders of magnitude of such effects are compared with those of other classical influences such as the Einstein redshift and transverse Doppler effects.