Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

TL;DR

This paper demonstrates that black holes with scalar hair in Lovelock-Galileon theories are universally unstable across all dimensions due to ghost and gradient instabilities near the horizon.

Contribution

It generalizes known five-dimensional black hole solutions to higher dimensions and proves their universal instability in Lovelock-Galileon theories.

Findings

Black hole solutions in five dimensions are unstable near the horizon.

The instability extends universally to higher dimensions.

The instability is due to ghost and gradient modes.

Abstract

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.