Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations

TL;DR

This paper analytically investigates the large frequency behavior of quasiperiodic perturbations in AdS spacetime, revealing exponential suppression and complex asymptotics, with implications for AdS stability and black hole formation.

Contribution

It provides a new analytic framework for understanding the frequency spectra of quasiperiodic AdS perturbations, especially at large mode numbers, including effects of gravity.

Findings

Quasiperiodic spectra exhibit exponential suppression modulated by a power law.

Analytic explanations for localized quasiperiodic solutions around a single mode.

Numerical evidence of logarithmic modulations in gravitational spectra.

Abstract

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.