AdS collapse of a scalar field in higher dimensions

Abstract

We point out that the weakly turbulent instability of anti-de Sitter space, recently found in [1] for four dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant, is present in all dimensions d + 1 for d ≥ 3, contrary to a claim made in [2].

Three-dimensional Gravity and Instability of AdS$_{3}$

“…Concentration of energy on finer spatial scales leads to gravitational collapse (black hole formation is the analogue of the viscous cut-off for fluids). Later, this result was extended in a straightforward manner to higher dimensions d > 3 [5] and verified and generalized to more general models [6,7,8,9]. In particular, the existence of time-periodic solutions was shown in [8,9].…”

“…In [4,5] it was found that small perturbations of AdS d+1 for d ≥ 3 generically evolve into a black hole. This instability of AdS has been conjectured to be caused by the resonant transfer of energy to high frequencies.…”

“…Following [4,5], in [1] we consider a simple asymptotically AdS solution in three dimensions, namely a self-gravitating spherically symmetric real massless scalar field. The dynamics of this solution is governed by the system of Einstein equations and the wave equation for the scalar field…”

Collapse and revival in holographic quenches

“…Different aspects of scalar collapse in AdS d+1 have been studied in [15,[21][22][23][24][25][26]. We will focus here on how the time invested on the first bounce depends on the mass and thickness of the initial shell.…”

“…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] …”