Gregory-Laflamme instability of black hole in Einstein-scalar-Gauss-Bonnet theories

TL;DR

This paper analyzes the stability of Schwarzschild black holes in Einstein-scalar-Gauss-Bonnet theory, revealing a Gregory-Laflamme type instability leading to scalar-haired black hole solutions in certain regimes.

Contribution

It identifies a new type of instability in Schwarzschild black holes within ESGB theory, linking it to Gregory-Laflamme instability and discovering bifurcating scalar-haired solutions.

Findings

Schwarzschild black hole becomes unstable for 1/λ<1.174/r_+

Instability is Gregory-Laflamme type, not tachyonic

Scalar-haired black hole solutions bifurcate from Schwarzschild

Abstract

We investigate the stability analysis of Schwarzschild black hole in Einstein-scalar-Gauss-Bonnet (ESGB) theory because the instability of Schwarzschild black hole without scalar hair implies the Gauss-Bonnet black hole with scalar hair. The linearized scalar equation is compared to the Lichnerowicz-Ricci tensor equation in the Einstein-Weyl gravity. It turns out that the instability of Schwarzschild black hole in ESGB theory is interpreted as not the tachyonic instability, but the Gregory-Laflamme instability of black string. In the small mass regime of $1/\lambda<1.174/r_+$, the Schwarzschild solution becomes unstable and a new branch of solution with scalar hair bifurcates from the Schwarzschild one. This is very similar to finding a newly non-Schwarzschild black hole in Einstein-Weyl gravity.