Collapse and Nonlinear Instability of AdS Space with Angular Momentum

Abstract

We present a numerical study of rotational dynamics in AdS5 with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the timescale for collapse at low energies E, keeping the angular momenta J ∝ E in AdS length units. We find that the inclusion of angular momenta delays the collapse time, but retains a t ∼ 1/E scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS appear stable, but those sufficiently far from AdS are unstable. We find that the dynamics of the boson star instability depend on the perturbation, resulting either in collapse to a Myers-Perry black hole, or development towards a stable oscillating solution.Introduction -Spacetimes with anti-de Sitter (AdS) boundary conditions play a central role in our understanding of gauge/gravity duality [1][2][3][4], where solutions to the Einstein equation with a negative cosmological constant are dual to states of strongly coupled field theories. This correspondence has inspired the study of gravitational physics in AdS over the past two decades.It is perhaps surprising that the issue of the nonlinear stability of (global) AdS was only raised nine years after AdS/CFT was first formulated [5,6]. Dafermos and Holzegel conjectured a nonlinear instability where the reflecting boundary of AdS allows for small but finite energy perturbations to grow and eventually collapse into a black hole. This is in stark contrast with Minkowksi and de Sitter spacetimes, where nonlinear stability has long been established [7,8].The first numerical evidence in favour of such an instability of AdS was reported in [9]. This topic has since attracted much attention both from numerical and formal perspectives . Remarkably, this instability has recently been proved for the spherically symmetric and pressureless Einstein-massless Vlasov system [62,63].The collapse timescale is dual to the thermalisation time in the field theory, and is important for characterising and understanding this instability. For energies E much smaller than the AdS length L = 1, early evolution is well-described by perturbation theory. However, irremovable resonances generically cause secular terms to grow, leading to a breakdown of perturbation theory at a time t ∼ 1/E. Numerical evidence suggests that horizon formation occurs shortly thereafter, i.e. at this same timescale. It is not fully understood why collapse seems to occur at the shortest timescale allowed by perturbation theory, though see [52] for some recent progress.However, all numerical studies have been restricted to zero angular momentum. Though perturbation theory breaks down at t ∼ 1/E for systems with rotation as well [10,53,64], this only places a lower bound on the timescale for gravitational collapse. It therefore remains unclear whether rotational forces could balance the gravitational attraction and delay the collapse time.The inc...

Floquet scalar dynamics in global AdS

“…4 also exhibit this modulated dynamics for one sign of the most relevant perturbation, and collapse to a black hole for the other. 3 Such behavior has been observed earlier, both in asymptotically flat [23] and AdS spacetime [24,25]. Also, SMS profiles like the one in Fig.…”

Charged black hole bombs in a Minkowski cavity

“…In the latter case, the mass of the bosonic field effectively provides a potential barrier that traps the bosonic waves near the horizon. From the superradiant studies in rotating AdS black holes it is conjectured that superradiant instabilities should evolve following one of two possible scenarios [12,[15][16][17][18][19][20].…”

Breathing Modes, Quartic Nonlinearities and Effective Resonant Systems

“…In relation to the concrete physical problems that have motivated our considerations, beyond what has been explicitly treated in the literature, one is led to expect solvable features in the resonant systems corresponding to (1) one-dimensional nonlinear Schrödinger equation in a harmonic trap with arbitrary 2-body interactions, (2) Landau-level truncations, in the style of [11], of nonlinear Schrödinger equations in isotropic harmonic traps with arbitrary 2-body interactions in any number of dimensions, (3) maximally rotating truncations of the resonant dynamics in AdS, in the style of [15], with arbitrary quartic local interactions. The last topic connects to extensive studies of nonlinear dynamics in AdS [21][22][23][24][25][26], in particular, outside spherical symmetry [27][28][29][30][31]. Some of the results presented here, in particular explicit analytic solutions within the resonant approximation, are specific to the case of quartic nonlinearities.…”