Solutions on a brane in a bulk spacetime with Kalb-Ramond field

TL;DR

This paper derives effective gravitational equations on a brane with a Kalb-Ramond field in the bulk, finding black hole solutions, analyzing stability, and exploring cosmological implications including accelerated expansion.

Contribution

It introduces the effects of a Kalb-Ramond field on brane gravity, deriving new solutions and analyzing their stability and cosmological behavior.

Findings

Black hole or naked singularity solutions depending on parameters

Kalb-Ramond field behaves as pressureless matter in cosmology

Possible accelerated expansion of the universe

Abstract

Effective gravitational field equations on a brane have been derived, when the bulk spacetime is endowed with the second rank antisymmetric Kalb-Ramond field. Since both the graviton and the Kalb-Ramond field are closed string excitations, they can propagate in the bulk. After deriving the effective gravitational field equations on the brane, we solve them for a static spherically symmetric solution. It turns out that the solution so obtained represents a black hole or naked singularity depending on the parameter space of the model. The stability of this model is also discussed. Cosmological solutions to the gravitational field equations have been obtained, where the Kalb-Ramond field is found to behave as normal pressure free matter. For certain specific choices of the parameters in the cosmological solution, the solution exhibits a transition in the behaviour of the scale factor and hence a transition in the expansion history of the universe. The possibility of accelerated expansion of the universe in this scenario is also discussed.