Eikonal instability of Gauss-Bonnet–(anti-)–de Sitter black holes

Here we have shown that asymptotically anti--de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, J. High Energy Phys. 07 (2016) 151 for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories Frolov, Phys. Rev. Lett. 115, 051102 (2015). The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.