On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions

TL;DR

This paper argues that many asymptotically anti-de Sitter solutions, including geons, boson stars, and black holes, are nonlinearly stable despite previous evidence of AdS instability, supported by quasinormal mode analysis.

Contribution

It introduces a stability analysis for various AdS solutions and discusses a new class of noncoalescing black hole binaries, challenging prior instability results.

Findings

Long-lived gravitational quasinormal modes identified

Many AdS solutions shown to be nonlinearly stable

New class of noncoalescing black hole binaries discussed

Abstract

Despite the recent evidence that anti-de Sitter spacetime is nonlinearly unstable, we argue that many asymptotically anti-de Sitter solutions are nonlinearly stable. This includes geons, boson stars, and black holes. As part of our argument, we calculate the frequencies of long-lived gravitational quasinormal modes of AdS black holes in various dimensions. We also discuss a new class of asymptotically anti-de Sitter solutions describing noncoalescing black hole binaries.