Scalar Quasinormal Modes of Anti-de Sitter Static Spacetime in Horava-Lifshitz Gravity with $U(1)$ Symmetry

TL;DR

This study explores how Hořava-Lifshitz gravity with $U(1)$ symmetry affects scalar quasinormal modes in Anti-de Sitter spacetime, revealing increased oscillation periods, slower decay, and potential instabilities.

Contribution

It derives static black hole solutions in Hořava-Lifshitz gravity and analyzes their impact on scalar quasinormal modes, highlighting the effects of gravitational corrections.

Findings

Hořava-Lifshitz correction increases quasinormal periods

Decay of oscillations is slowed by the correction

Scalar field may become unstable with large corrections

Abstract

In this paper, we investigate the scalar quasinormal modes of Ho\v{r}ava-Lifshitz theory with $U(1)$ symmetry in static Anti-de Sitter spacetime. The static planar and spherical black hole solutions in lower energy limit are derived in non-projectable Ho\v{r}ava-Lifshitz gravity. The equation of motion of a scalar field is obtained, and is utilized to study the quasinormal modes of massless scalar particles. We find that the effect of Ho\v{r}ava-Lifshitz correction is to increase the quasinormal period as well as to slow down the decay of the oscillation magnitude. Besides, the scalar field could be unstable when the correction becomes too large.