Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb-Ramond field

TL;DR

This paper studies how a background Kalb-Ramond field influences the geodesic structure, deflection angles, and observable properties of charged black holes, revealing effects similar to high-spin Kerr black holes and implications for astrophysical measurements.

Contribution

It provides a detailed analysis of geodesics, photon spheres, and deflection angles in charged black holes with Lorentz-violating fields, highlighting novel effects and potential observational signatures.

Findings

Lorentz-violating parameter mimics high spin Kerr black holes.

Decreased center of mass energy with increasing Lorentz violation.

Stable circular orbits are sensitive to Lorentz-violating effects.

Abstract

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb-Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge ($Q$) and the Lorentz-violating parameter ($b$) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., $a/M \sim 1$ thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both $b$ and $Q$ increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters $b$ and $Q$. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss-Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.