Gregory-Laflamme instability of black hole in Einstein-scalar-Gauss-Bonnet theories
arXiv:1805.05023 · doi:10.1103/PhysRevD.98.024030
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 , 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.
14 pages, 4 figures, version to appear in Physical Review D
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