Nonminimal derivative coupling scalar-tensor theories: odd-parity perturbations and black hole stability

TL;DR

This paper analyzes the stability of hairy black holes in a specific class of scalar-tensor theories with nonminimal kinetic coupling, deriving perturbation equations and demonstrating mode stability under odd-parity perturbations.

Contribution

It derives the odd parity perturbation equations and potential for black holes in nonminimal kinetic coupling Horndeski theories, proving their mode stability.

Findings

Mode stability of hairy black holes established

Perturbation potential derived in tortoise coordinates

Implications for rotating black holes and neutron stars discussed

Abstract

We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd- parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solutions in this setup and discuss their implications on the physics of compact objects configurations, such as neutron stars.