Black hole quasinormal modes in a scalar-tensor theory with field derivative coupling to the Einstein tensor

TL;DR

This paper studies the quasinormal modes of scalar fields around black holes in a scalar-tensor theory with derivative coupling, revealing how these modes depend on black hole size and cosmological constant in an asymptotically AdS spacetime.

Contribution

It provides numerical analysis of quasinormal frequencies in a scalar-tensor theory with derivative coupling, extending understanding beyond general relativity and Schwarzschild-AdS solutions.

Findings

Quasinormal frequencies match Schwarzschild-AdS for tuned parameters.

Large black holes show insensitivity to the cosmological constant.

Small black holes exhibit decreasing real frequency with increasing cosmological constant.

Abstract

We investigate the quasinormal modes of a test massless, minimally coupled scalar field on a static and spherically symmetric black hole in the scalar-tensor theory with field derivative coupling to the Einstein tensor, which is a part of the Horndeski theory with the shift symmetry. In our solution, the spacetime is asymptotically AdS (anti-de Sitter), where the effective AdS curvature scale is determined solely by the derivative coupling constant. The metric approaches the AdS spacetime in the asymptotic infinity limit and precisely recovers the Schwarzschild-AdS solution in general relativity if the coupling constant is tuned to the inverse of the cosmological constant. We numerically find the lowest lying quasinormal frequency for the perturbation about a test massless, minimally coupled scalar field. The quasinormal frequency agrees with that of the Schwarzschild-AdS solution for the tuned case. For other parameters, in the large black hole limit, as the metric coincides with that of the Schwarzschild-AdS black hole, the quasinormal frequency almost agrees with that of the Schwarzschild-AdS black hole and is insensitive to the value of the cosmological constant. On the other hand, for a small back hole the real part of the quasinormal frequency decreases as the absolute value of the cosmological constant increases.