Existence and Instability of Novel Hairy Black Holes in Shift-symmetric Horndeski Theories

TL;DR

This paper demonstrates that black holes with time-dependent scalar hair in shift-symmetric Horndeski theories are inherently unstable due to gradient instabilities in scalar perturbations, ruling out their physical viability.

Contribution

It provides a detailed perturbation analysis showing the instability of these black holes, extending previous results and conclusively ruling out their existence in these theories.

Findings

Scalar perturbations exhibit gradient instabilities

Time-dependent scalar hair black holes are ruled out

Instability persists across analyzed solutions

Abstract

Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild black hole solutions exhibiting time-dependent scalar hair. By making use of Lema\^{i}tre coordinates, we analyze perturbations around these types of black holes, and demonstrate that scalar perturbations around black hole backgrounds inevitably have gradient instabilities. Taken together with previously established results, this newly-discovered instability rules out black holes with time-dependent scalar hair in Horndeski theories.