Traversable wormhole solution with a background Kalb-Ramond field

TL;DR

This paper presents a new static spherically symmetric traversable wormhole solution influenced by a background Kalb-Ramond field, which breaks Lorentz symmetry and affects light deflection.

Contribution

It introduces an exact wormhole solution with Lorentz symmetry breaking from a Kalb-Ramond field and analyzes its physical and observational properties.

Findings

Wormhole solution supported by matter with negative isotropic pressure.

Matter satisfies energy conditions at the throat for specific Lorentz symmetry breaking parameters.

Calculated light deflection angle in the weak limit approximation.

Abstract

We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (VEV) of a Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (VEV) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss-Bonnet method to analyze the deflection angle of light in the weak limit approximation.