Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes

TL;DR

This paper studies the effects of a Kalb-Ramond field on rotating black holes, analyzing their shadows and light deflection, and constrains the field parameters using observations of M87* and Sgr A*.

Contribution

It derives a new rotating black hole solution with a Kalb-Ramond field and analyzes its shadow and light deflection, providing observational bounds on the field parameters.

Findings

Black hole shadow size decreases with increasing Kalb-Ramond parameter.

Shadows are more distorted than Kerr black holes.

Constraints on the Kalb-Ramond field parameter from M87* and Sgr A* observations.

Abstract

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb-Ramond field with gravity leads to a power-law hairy black hole having a parameter $s$, which encompasses the Reissner$-$Nordstrom black hole ($s=1$). We obtain the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb-Ramond black hole, which encompasses, as special cases, Kerr ($s=0$) and Kerr-Newman ($s=1$) black holes. Interestingly, for a set of parameters ($M, a$, and $\Gamma$), there exists an extremal value of the Kalb-Ramond parameter ($s=s_{e}$), which corresponds to an extremal black hole with degenerate horizons, while for $s<s_{e}$, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for $s>s_{e}$. We find that the extremal value $s_e$ is also influenced by these parameters. The black hole shadow size decreases monotonically and the shape gets more distorted with an increasing $s$; in turn, shadows of rotating Kalb-Ramond black holes are smaller and more distorted than the corresponding Kerr black hole shadows. We investigate the effect of the Kalb-Ramond field on the rotating black hole spacetime geometry and analytically deduced corrections to the light deflection angle from the Kerr and Schwarzschild black hole values. The deflection angle for Sgr A* and the shadow caused by the supermassive black hole M87* are included and compared with analogous results of Kerr black holes. The inferred circularity deviation $\Delta C\leq 0.10$ for the M87* black hole merely constrains the Kalb-Ramond field parameter, whereas shadow angular diameter $\theta_d=42\pm 3\, \mu$as, within the $1\sigma$ region, places bounds $\Gamma\leq 0.09205$ for $s=1$ and $\Gamma\leq 0.02178$ for $s=3$.