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

Understand

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.