Gravitational instantons of Bianchi type IX space are constructed in Ashtekar’s canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the “initial surface” and “Hamiltonian equations”. This formallism is applicable to the matter coupled system with cosmological constant.

The Bianchi type I cosmological model is brought into a form where the evolution of observables is governed by the unconstrained Hamiltonian that coincides with the Hamiltonian describing the relative motion of particles in the integrable three-body hyperbolic Euler-Calogero-Sutherland system.

Some Bianchi type I cosmological models of the universe with time dependent gauge function β for viscous fluid distribution within the framework of Lyra geometry are investigated in which the expansion is considered only in two dimensions i.e. one of the Hubble parameter (H1 = Ȧ A) is zero. To get the deterministic solutions of Einstein’s modified field equations, the viscosity coefficient of b...

General Relativity describes the state in which radiation concentrates around a star. Klein (1948) worked on it and obtained an approximate solution to Einsteinian field equations in spherical symmetry for a distribution of diffused radiation. Many other researchers (Singh and Abdussattar, 1973; Roy and Bali, 1977) have worked on this topic and obtained exact static spherically and cylindricall...

A considerable interest has been shown to the study of physical properties of spacetimes which are conformal to certain well known gravitational fields. The general theory of relativity is believed by a number of unknown functions the ten components of g . Hence there is a little hope of finding physically interesting results without making reduction in their number. In conformally flat spaceti...

Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein’s equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston’s H × R) type, while the other is the Bianchi II (Thurston’s Nil) type. With a brief summary of previous results on the Bianchi III perturbations, as...

The cosmic, general analitic solutions of the Brans–Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions –which includes cosmological models with the open and the closed spaces of the Friedmann–Robertson–Walker metric, as well as solutions for models with homogeneous but anisotropic spaces cor...