Stability of Anti–de Sitter Space in Einstein-Gauss-Bonnet Gravity

Abstract

Recently it has been argued that in Einstein gravity anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass-energy content of the spacetime is too small, thereby restoring the stability of anti-de Sitter spacetime in this context. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity

“…We see a stepwise structure of delayed collapses. In the physical d = 3 case, our plots resemble those of wide initial gaussians in AdS [35], or those of theories with a mass gap for BH formation, such as AdS 3 [36], Einstein-Maxwell-scalar [37] or EinsteinGauss-Bonnet [38,39]. There are plateaux for which collapses occur after a number of bounces and transition regions where the collapsing time becomes a chaotic function of the initial amplitude.…”

“…in [35], 3 in [57], 16 in [37] or 2 in [38]). The chaotic character of the curve at the bumps has been recently established in [39].…”

Gravitational geons in asymptotically anti-de Sitter spacetimes

“…As a valid first order solution, we can choose any linear combination of the metric perturbations generated by equations (14) and (15), with arbitrary amplitudes and phases, for a number of different (l, m). Proceeding to second order in ε, there will be Φ (s,v)(0) source terms appearing in Equation (10) for certain scalar and vector (l, m) cases.…”

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

“…A way to stabilize the AdS space-time is known: collapse of the perturbation energy, what ends up with a stable AdS black hole in Einstein theory. In [19] it was shown that adding the Gauss-Bonnet correction prevents formation of the black hole with small mass, what was interpreted as the stability gap of AdS space-times in GB theory [19].…”

“…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 Gauss-Bonnet term, it was shown [19] that 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 [20].…”