Quasinormal modes of a scalar perturbation coupling with Einstein's tensor in the warped $AdS_3$ black hole spacetime

TL;DR

This paper investigates how a scalar field coupled to Einstein's tensor behaves in a warped $AdS_3$ black hole, revealing dependencies of quasinormal modes on the coupling and warped parameter, and exploring implications for the warped $AdS/CFT$ correspondence.

Contribution

It introduces the analysis of scalar perturbations coupled to Einstein's tensor in warped $AdS_3$ black holes, highlighting their effects on quasinormal modes and dual conformal weights.

Findings

Quasinormal frequencies depend on the warped parameter and coupling.

Coupling influences the conformal weights in the dual CFT.

The study provides insights into warped $AdS/CFT$ correspondence effects.

Abstract

We have studied the quasinormal modes of a massive scalar field coupling to Einstein's tensor in the spacelike stretched $AdS_3$ black hole spacetime. We find that both the right-moving and left-moving quasinormal frequencies depend not only on the warped parameter $v$ of black hole, but also on the coupling between the scalar field and Einstein's tensor. Moreover, we also discuss the warped $AdS/CFT$ correspondence from the quasinormal modes and probe the effects of the coupling on the left and right conformal weights $h_L$ and $h_R$ of the operators dual to the scalar field in the boundary.