Spherical shells of fluid in general relativity are considered. The density is assumed to be spatially uniform and it is found that there may be three cases of positive, negative and vanishing Schwarzschild mass of the shell although the density and the pressure are both positive throughout. However the negative mass case has to be associated with a singularity representing a negative mass particle and so is unphysical. The zero mass solution has the intriguing feature that the geometry on either side of the shell is Minkowskian and the space is closed. This closure of the space saves the present result from being in contradiction with the positive energy theorems. Earlier investigations claiming zero-mass distributions are also discussed.

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.

A brief account for the higher order wave function in Hartle-Hawking (H-H) proposal is given which is compared with the tunneling wave function due to Vilenkin. The probability distributions are determined for both types of wave functions. Also a class of solutions are evaluated using H-H approach for Kantowski-Sachs metric with a scalar field and inflation is observed.

The compactification of 10-dimensional supergravity, coupled to super Yang-Mills theory, to curved 4-dimensional spacetimes is investigated. The requirement of unbroken supersymmetry leads to a set of consistency conditions. These are fairly restrictive, but nevertheless permit some nontrivial solutions, including the Milne universe. More general time-dependent metrics are also not ruled out.

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed.

The properties of a configuration of two scalar doublets admitting a global SO(2) symmetry is studied in the presence of an abelian dyon core when the scalar doublets are coupled to the electromagnetic field through parity violating and parity preserving terms. The mass and the conserved global charge of theQ configuration are computed in terms of the parameters of the lagrangian.

We propose a formalism for the study of mean resistance of a one dimensional chain of random potentials. We obtain the resistance as a function of the length of the chain. In the asymptotic limit, this is related to the wavefunction envelope. The formalism demands loss of translational symmetry, but is general enough to include potentials with spatial correlations which are not long ranged and also those whose randomness is inhomogeneous.

K- and L-shell ionization cross sections of gold due to impact of proton and alpha particles have been calculated in the binary encounter approximation incorporating the effects of Coulomb deflection of the projectile, of increase in binding of the target electron, and of polarization and relativity. Relativistic Hartree-Fock-Roothaan (RHFR) momentum distributions for the target electron along with an approximate relativistic correction to the collision dynamics have been used in the present calculations. A comparison with the corresponding calculations using non-relativistic Hartree-Fock-Roothaan wave functions, experimental results and other available calculations is presented.