Stability of Hairy Black Holes in Shift-Symmetric Scalar-Tensor Theories via the Effective Field Theory Approach

TL;DR

This paper develops an effective field theory framework to analyze the stability of hairy black holes in shift-symmetric Horndeski theories, deriving constraints for stable solutions and examining perturbations.

Contribution

It introduces a novel EFT approach in Lemaître coordinates to study stability conditions of hairy black holes in shift-symmetric scalar-tensor theories.

Findings

Derived stability constraints for Horndeski functions

Analyzed decoupling limit for instability sources

Performed perturbation analysis for spherically symmetric spacetimes

Abstract

Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild-de Sitter black hole solutions exhibiting time-dependent scalar hair. The properties of these solutions may be studied via a bottom-up effective field theory (EFT) based on the background symmetries. This is in part possible by making use of a convenient coordinate choice -- Lema\^itre-type coordinates -- in which the profile of the Horndeski scalar field is linear in the relevant time coordinate. We construct this EFT, and use it to understand the stability of hairy black holes in shift-symmetric Horndeski theories, providing a set of constraints that the otherwise-free functions appearing in the Horndeski Lagrangian must satisfy in order to admit stable black hole solutions. The EFT is analyzed in the decoupling limit to understand potential sources of instability. We also perform a complete analysis of the EFT with odd-parity linear perturbations around general spherically symmetric space-time.