AdS (In)stability: Lessons From The Scalar Field

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.

arXiv comment10 pages, 4 figures

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• Collapse and Nonlinear Instability of AdS with Angular Momenta
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• Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
• AdS nonlinear instability: moving beyond spherical symmetry
• Phases of Global AdS Black Holes
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
• Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes
• Collapse of self-interacting scalar field in anti-de Sitter space
• Necessary conditions for an AdS-type instability
• Coherent Cascade Conjecture for Collapsing Solutions in Global AdS
• Fully resonant scalars on asymptotically AdS wormholes
• AdS nonlinear instability: breaking spherical and axial symmetries
• New islands of stability with double-trace deformations
• Detailed ultraviolet asymptotics for AdS scalar field perturbations
• Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime
• Gravitational systems in asymptotically anti-de Sitter space-times
• Gravitational Perturbations in a cavity: Nonlinearities
• Nonlinear perturbations of higher dimensional anti-de Sitter spacetime
• Old and New Scaling Laws in Quantum Quench