Weakly Turbulent Instability of Anti–de Sitter Spacetime

Abstract

We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) space by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS space is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.

Collapse and revival in holographic quenches

“…A spherical matter shell which does not carry enough energy density to create a horizon as it implodes, will scatter away. However in an asymptotically AdS geometry, the shell will bounce back and start a new infall [14,15]. In [16] it was proposed that such bouncing geometries provide the holographic counterpart to processes which exhibit quantum revivals.…”

“…When reflecting conditions are imposed at the AdS boundary, x = π/2, an expanding shell will bounce against it and start a new infall [14,15]. Such implosion-expansion cycles can repeat several times.…”

“…This is indeed the case for the collapse of null dust, which is described by explicit solutions of the Einstein equations known as Vaidya metrics. In this paper we will consider instead a scalar field profile, whose infall is known not to always lead to black hole formation [14,15].…”

“…The minima of A m (t) correspond to the moments of maximal implosion of the matter shell and the maxima to its bounces against the AdS boundary, see figure 2. Following previous works [15,[21][22][23][24][25][26], we will consider a matter shell composed of a massless scalar field. The equations of motion for the system are [15] …”

“…Hence we are led to study gravitational collapse of a spherically symmetric matter distribution. A convenient ansatz for the metric is [15] …”