Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium

TL;DR

This paper studies how scalar fields decay around AdS black holes by analyzing quasinormal modes, revealing exponential decay without power-law tails, and computes thermalization timescales in dual strongly coupled field theories.

Contribution

It provides the first detailed analysis of quasinormal modes for AdS black holes across multiple dimensions and links decay times to thermalization in dual field theories.

Findings

Decay is exponential with no late-time power-law tails.

Decay timescales are computed for 3, 4, and 6-dimensional dual theories.

Results inform the approach to thermal equilibrium in strongly coupled systems.

Abstract

We investigate the decay of a scalar field outside a Schwarzschild anti de Sitter black hole. This is determined by computing the complex frequencies associated with quasinormal modes. There are qualitative differences from the asymptotically flat case, even in the limit of small black holes. In particular, for a given angular dependence, the decay is always exponential - there are no power law tails at late times. In terms of the AdS/CFT correspondence, a large black hole corresponds to an approximately thermal state in the field theory, and the decay of the scalar field corresponds to the decay of a perturbation of this state. Thus one obtains the timescale for the approach to thermal equilibrium. We compute these timescales for the strongly coupled field theories in three, four, and six dimensions which are dual to string theory in asymptotically AdS spacetimes.