Some exact solutions in curved spacetimes of n 4 dimensions

Abstract

This thesis consists of ten papers divided into the following five parts : I String cosmologies II Some other cosmologies III Higher dimensions IV Geodetic precession V Broken-symmetry theory of gravity In part I some Bianchi type cosmological models are studied in the context of cosmic strings. In the first paper of this part Letelier model is studied in the context of Bianchi types II, VIo, VIII and IX cosmologies. In the second paper a study of cosmic strings is presented in four-dimensional Bianchi type III and V cosmologies and in ( n+1 ) dimensional Bianchi type I cosmology. It is interesting to note that cosmic strings do not occur in Bianchi type V cosmology. This part is closed with a brief report by demonstrating that cosmic string-like structures are intrinsic to a class of Godel space-times. In part II some other cosmologies are studied. In the first paper of this part an alternatives view of cosmology with variable G and A is presented. The consequences of the idea that the principle of equivalence, which rests on the experimentally established equality of inertial mass and gravitational mass, might not be valid in an early phase of the universe is also explored. In the next paper cosmological solutions for Bianchi type I metric are derived in general scalar-tensor gravity theories including Brans-Dicke gravity for vaccum, stiff matter and radiation. It is further shown that as the scalar field evolves the anisotropy decays much faster than the energy-density. In part III some solutions in Einstein-Kalb-Ramond cosmology in (9+1) dimensions, charged solutions in higher dimensions and Blackholes coupled to scalar fields in higher-dimensional Kaluza-Klein theory are presented. In the first paper of this part some cosmological solutions of Einstein-Kalb-Ramond equations are investigated with and without matter in ( 9+1 ) dimensions. One of the two solutions with matter corresponds to isotropic three-space and the other to anisotropic three space. The additional six-space shrinks with the evolution of...