343 research outputs found
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
A spacetime dual to the NUT spacetime
By decomposing the Riemann curvature into electric and magnetic parts, a
duality transformation, which involves interchange of active and passive
electric parts, has recently been proposed. It was shown that the Schwarzschild
solution is dual to the one that describes the Schwarzschild particle with
cloud of string dust or a global monopole. Following the same procedure we
obtain the solution dual to the NUT spacetime.Comment: 10 pages, Latex. Accepted for publication in Classical and Quantum
Gravit
Non-singular black-holes on the brane
We investigate the possibility of obtaining non-singular black-hole solutions
in the brane world model by solving the effective field equations for the
induced metric on the brane. The Reissner-Nordstrom solution on the brane was
obtained by Dadhich etal by imposing the null energy condition on the 3-brane
for a bulk having non zero Weyl curvature. In this work, we relax the condition
of vanishing scalar curvature , however, retaining the null condition. We
have shown that it is possible to obtain class of static non-singular
spherically symmetric brane space-times admitting horizon. We obtain one such
class of solution which is a regular version of the Reissner-Nordstrom solution
in the standard general relativity.Comment: 8 pages, References added, Version to appear in Int. J. Mod. Phys.
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
Oscillating non-singular relativistic spherical model
A particular choice of the time function in the recently presented spherical
solution by Dadhich [1] leads to a singularity free cosmological model which
oscillates between two regular states. The energy-stress tensor involves
anisotropic pressure and a heat flux term but is consistent with the usual
energy conditions (strong, weak and dominant). By choosing the parameters
suitably one can make the model consistent with observational data. An
interesting feature of the model is that it involves blue shifts as in the
quasi steady state model [2] but without violating general relativity.Comment: 6 pages, REVTEX versio
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
Singularity: Raychaudhuri Equation once again
I first recount Raychaudhuri's deep involvement with the singularity problem
in general relativity. I then argue that precisely the same situation has
arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered
his celebrated equation. We thus need a new analogue of the Raychaudhuri
equation in quantum gravity.Comment: 11 pages, Contribution to Special issue of Pramana on Raychaudhuri
Equation at Cross-roads, edited by Naresh Dadhich, Pankaj Joshi and Probir
Ro
Singularity free cosmological solutions of Einstein-Maxwell equations
We report on a new two-parameter class of cosmological solutions to the
Einstein-Maxwell equations. The solutions have everywhere regular curvature
invariants. We prove that the solutions are geodesically complete and globally
hyperbolic.Comment: 8 pages,latex; v2 some typos correcte
Inhomogeneous imperfect fluid spherical models without Big-Bang singularity
So far all known singularity-free cosmological models are cylindrically
symmetric. Here we present a new family of spherically symmetric non-singular
models filled with imperfect fluid and radial heat flow, and satisfying the
weak and strong energy conditions. For large anisotropy in pressure and
heat flux tend to vanish leading to a perfect fluid. There is a free function
of time in the model, which can be suitably chosen for non-singular behaviour
and there exist multiplicity of such choices.Comment: 8 pages, LaTeX versio
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