AdS (In)stability: Lessons From The Scalar Field

TL;DR

This paper investigates the scalar field in Anti-de Sitter space using the Two-Time Formalism, providing evidence that energy distribution remains non-thermalized over certain timescales, which may imply stability against collapse.

Contribution

It demonstrates that in the TTF framework, higher mode energies are exponentially suppressed, suggesting no thermalization occurs within specific time-scales for scalar fields in AdS.

Findings

Higher modes are exponentially suppressed at late times.

No thermalization occurs within timescales ~1/ε².

Potential implications for AdS gravitational stability.

Abstract

We argued in arXiv:1408.0624 that the quartic scalar field in AdS has features that could be instructive for answering the gravitational stability question of AdS. Indeed, the conserved charges identified there have recently been observed in the full gravity theory as well. In this paper, we continue our investigation of the scalar field in AdS and provide evidence that in the Two-Time Formalism (TTF), even for initial conditions that are far from quasi-periodicity, the energy in the higher modes at late times is exponentially suppressed in the mode number. Based on this and some related observations, we argue that there is no thermalization in the scalar TTF model within time-scales that go as $\sim 1/\epsilon^2$, where $\epsilon$ measures the initial amplitude (with only low-lying modes excited). It is tempting to speculate that the result holds also for AdS collapse.