Quasi-normal modes of black holes in scalar-tensor theories with non-minimal derivative couplings

TL;DR

This paper investigates how scalar-tensor theories with non-minimal derivative couplings alter the quasi-normal mode spectrum of anti-de Sitter black holes, revealing differences from classical general relativity predictions.

Contribution

It provides the first numerical analysis of quasi-normal modes in shift-symmetric Horndeski theories with derivative couplings to the Einstein tensor.

Findings

Different effective potential compared to Schwarzschild-AdS

Altered quasi-normal mode spectrum in scalar-tensor theories

Distinct signatures for minimally and non-minimally coupled scalars

Abstract

We study the quasi-normal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The space-time differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasi-normal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and non-minimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found in general relativity.