Electromagnetic duality in general relativity

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio

Global monopole as dual-vacuum solution in Kaluza-Klein spacetime

By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in 4-dimensional Euclidean space and would have massless limit analogus to the 4-dimensional dual-flat solution.Comment: 8 pages, LaTEX versio

Gravitational Collapse in Constant Potential Bath

We analyse here the gravitational collapse of directed null radiation in a background with a constant potential such as one produced by a star system like galaxy in which the collapsing object is immersed. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. An interesting feature that emerges is that a part of the naked singularity spectrum in collapsing Vaidya region gets covered in the corresponding dual-Vaidya region, which corresponds to the Vaidya directed null radiation sitting in constant potential bath. The implications of such a result towards the issue of stability of naked singularities are discussed.Comment: LaTex 12 Pages, 2 figures. To appear in Physical Review

String-Dust Distributions with the Kerr-NUT symmetry

We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of the Kerr and the NUT solutions. There also occurs an interesting case of radiating string-dust which arises from string-dust generalization of Vaidya's solution of a radiating star.Comment: 15 pages, TeX version. tex error correcte

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 G\ddot o del 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