Quasinormal modes of a scalar perturbation around a rotating BTZ-like black hole in Einstein-bumblebee gravity

TL;DR

This paper analytically investigates the quasinormal modes of scalar perturbations around a rotating BTZ-like black hole in Einstein-bumblebee gravity, revealing how Lorentz symmetry breaking affects decay rates and conformal weights in the AdS/CFT correspondence.

Contribution

It provides the first analytical study of quasinormal modes in Einstein-bumblebee gravity, showing the impact of Lorentz symmetry breaking on mode decay and boundary conformal weights.

Findings

Lorentz symmetry breaking parameter affects imaginary parts of frequencies

Perturbation decay rate varies with the sign of the Lorentz parameter

Lorentz parameter influences conformal weights in AdS/CFT correspondence

Abstract

We analytically study the quasinormal modes of a scalar perturbation around a rotating BTZ-like black hole in the Einstein-bumblebee gravity. We observe that the Lorentz symmetry breaking parameter imprints only in the imaginary parts of the quasinormal frequencies for the right-moving and left-moving modes. The perturbational field decays more rapidly for the negative Lorentz symmetry breaking parameter, but more slowly for the positive one. The forms of the real parts are the same as those in the usual BTZ black holes. Moreover, we also discuss the $AdS/CFT$ correspondence from the quasinormal modes and find that the Lorentz symmetry breaking parameter enhances the left and right conformal weights $h_L$ and $h_R$ of the operators dual to the scalar field in the boundary. These results could be helpful to understand the $AdS/CFT$ correspondence and the Einstein-bumblebee gravity with the Lorentz symmetry violation.