Exact black hole solutions in gravity with a background Kalb-Ramond field

TL;DR

This paper derives exact static and rotating black hole solutions in a Lorentz-violating gravity theory with a background Kalb-Ramond field, and analyzes their thermodynamic properties.

Contribution

It provides the first exact solutions for black holes in gravity theories with a background Kalb-Ramond field and examines their thermodynamics.

Findings

Standard thermodynamic laws hold for these black holes.

Exact solutions for static and rotating black holes are obtained.

Thermodynamic relations like the first law and Smarr formula remain valid.

Abstract

In this work, we derive exact solutions for four-dimensional static spherically symmetric black holes and three-dimensional rotating black holes within a Lorentz-violating gravity theory. In this framework, Lorentz symmetry is spontaneously broken when a nonminimally coupled Kalb-Ramond tensor field acquires a nonzero vacuum expectation value. Building upon these solutions, we investigate the thermodynamic properties of the black holes using the Iyer-Wald formalism. Our findings reveal that the standard first law of thermodynamics and the Smarr relation remain valid for black holes in the presence of the Kalb-Ramond field.