Lorentz symmetry violating BTZ black holes in massive gravity

TL;DR

This paper explores how coupling a bumblebee field with massive gravity modifies BTZ black holes, leading to new solutions that exhibit Lorentz symmetry violation and diverse asymptotic behaviors, with thermodynamic properties analyzed.

Contribution

It introduces a family of static BTZ black hole solutions in massive gravity coupled with a bumblebee field, demonstrating Lorentz symmetry violation effects.

Findings

Solutions describe asymptotically AdS or de Sitter black holes

Lorentz symmetry violation influences black hole properties

Thermodynamics of modified black holes is analyzed

Abstract

BTZ black holes provide excellent frameworks for studying theories that are at the interface of classical and quantum gravity. In this paper we couple the Riemannian spacetime with the bumblebee field, in the background of massive gravity, which produces the violation of spontaneous Lorentz symmetry. In this setup we construct a large family of static vacuum BTZ black hole solutions. We study the asymptotic behaviour of curvature invariants and show that our resulting solutions describe asymptotically AdS (2+1)-dimensional BTZ black holes with negative cosmological constant. For positive cosmological constant they are de Sitter. Thermodynamics of these black holes is also analysed.