Rapid Thermalization in Field Theory from Gravitational Collapse

TL;DR

This paper investigates gravitational collapse in AdS space to understand rapid thermalization in dual field theories, finding that black hole formation and thermalization occur quickly across various initial conditions.

Contribution

It provides a numerical study linking scalar field collapse in AdS to rapid thermalization in dual field theories, highlighting the dependence on initial conditions.

Findings

Small initial amplitudes do not form black holes, resulting in oscillatory scalar fields.

Large initial amplitudes lead to black hole formation, indicating thermalization.

Thermalization occurs near the causal bound for a wide range of black hole masses.

Abstract

Motivated by the duality with thermalization in field theory, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. We investigate the system numerically and establish that for small values of the initial amplitude of the scalar field there is no black hole formation, rather, the scalar field performs an oscillatory motion typical of geodesics in AdS. For large enough values of the amplitude of the scalar field we find black hole formation which we detect numerically as the emergence of an apparent horizon. Using the time of formation as an estimate for thermalization in the field theory we conclude that thermalization occurs very rapidly, close to the causal bound for a very wide range of black hole masses. We further study the thermalization time in more detail as a function of the amplitude and the width of the initial Gaussian scalar field profile and detect a rather mild structure.