L. K. Patel

Some exact solutions of string cosmology in Bianchi III space-time

Following the techniques used by Letelier and Stachel some exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed. Some string solutions in which magnetic fields are absent are also discussed.

Some exact solutions in Bianchi VI0 string cosmology

Following the techniques used by Letelier and Stachel some new physically relevant explicit Bianchi VI0 solutions of string cosmology with magnetic field are reported. They include two models describing distributions of Takabayashi strings and geometric strings respectively.

A class of cylindrically-symmetric models in string cosmology

A new class of physically relevant explicit solutions for string cosmological models endowed with cylindrical symmetry on the background of singularity-free cosmological space times has been obtained and their physical and kinematical features are discussed. The matter-free limits of this class of solutions are observed to be the singularity-free vacuum solutions of Patel and Dadhich.

A charged analogue of the Vaidya-Tikekar solution

We present here an interior solution of the Einstein-Maxwell equations for a charged static fluid sphere. The physical 3-space t = constant of the solution is spheroidal. The solution is interpreted as an exact relativistic model for a charged superdense star.

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed.

A duality relation for fluid spacetime

We consider the electromagnetic resolution of the gravitational field. We show that under the duality transformation, in which active and passive electric parts of the Riemann curvature are interchanged, a fluid spacetime in comoving coordinates remains invariant in character with density and pressure transforming, while energy flux and anisotropic pressure remain unaltered. Furthermore, if the fluid admits a barotropic equation of state, where , which will transform to . Clearly the stiff fluid and dust are dual to each other, while will go to flat spacetime. However, the radiation and the de Sitter universes are self-dual.

Some Bianchi type VI 0 viscous fluid cosmological models

The Einstein field equations have been solved for Bianchi type VI 0 spacetimes with viscous fluid source. Four cosmological models are derived. They have nonzero expansion and shear. One of them have nonzero constant shear viscosity coefficient.

Radiating Kerr particle in Einstein universe

A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field.

Gravoelectric-dual of the Kerr solution

By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way that it still admits the Kerr solution but is not duality invariant. The dual equation is then solved to obtain the dual-Kerr solution which can be interpreted as the Kerr black hole sitting in a string dust universe.

A class of stationary rotating string cosmological models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.