Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime

TL;DR

This paper investigates the stability of initial data in anti-de Sitter spacetime for massless and massive scalar fields, revealing that known stable configurations are dominated by single modes and identifying new stable solutions with multi-mode energy distribution.

Contribution

It provides the first comprehensive analysis of stable initial data for massive scalars, extending understanding beyond the previously known single-mode dominated stability in massless cases.

Findings

Stable massless scalar initial data are dominated by single eigenmodes.

Numerical evidence suggests collapse time scales inversely with the square of the amplitude.

Discovery of a new class of stable or quasi-stable solutions for massive scalars with multi-mode energy distribution.

Abstract

Since horizon formation in global anti-de Sitter spacetime is dual to thermalization of a conformal field theory on a compact space, whether generic initial data is stable or unstable against gravitational collapse is of great interest. We argue that all the known stable initial data for massless scalars are dominated by single scalar eigenmodes, specifically providing strong numerical evidence consistent with the interpretation that initial data with equal energies in two modes collapse on time scales of order the inverse square of the amplitude. We further scan the parameter space for massive scalar field initial data and present evidence for a novel class of stable or quasi-stable solutions for massive scalars with energy spread through several eigenmodes.