Gravitational lensing of a Schwarzschild-like black hole in Kalb-Ramond gravity

TL;DR

This paper analyzes gravitational lensing effects around a Schwarzschild-like black hole influenced by a Kalb-Ramond field, providing exact deflection angles and potential observational signatures for future measurements.

Contribution

It introduces a novel exact calculation of deflection angles in a Kalb-Ramond black hole spacetime and explores observable effects relevant for astrophysical measurements.

Findings

Increasing the KR parameter decreases the deflection angle.

Derived exact deflection angles for massive and massless particles.

Predicted observable signatures in the weak field regime for Sagittarius A*.

Abstract

In this paper, we investigate the gravitational lensing effect for the Schwarzschild-like black hole spacetime in the background of a Kalb-Ramond (KR) field proposed in [K. Yang et. al., Phys. Rev. D 108 (2023) 124004]. The solution is characterized by a single extra parameter $l$, which is associated to the Lorentz symmetry breaking induced by the KR field. First, we calculate the exact deflection angle of massive and massless particles for finite distances using elliptic integrals. Then we study this effect in the weak and strong field regimes, discussing the correction of the KR parameter on the coefficients of the expansions in both limits. We also find that increasing $l$ decreases the deflection angle. Furthermore, we use the available data from the Sagittarius $A^{\star}$ object, which is believed to be a supermassive black hole at the center of our galaxy, to calculate relevant observables, such as, the image position, luminosity, and delay time. The values found could be potentially measured in the weak field regime, though for strong fields one would have to wait for the next generation of interferometers.