Thermalization with a chemical potential from AdS spaces

TL;DR

This paper investigates the thermalization process in holographic models with a chemical potential, revealing how charge influences thermalization times using AdS space models and various probes.

Contribution

It systematically analyzes the impact of black hole charge on thermalization times in AdS/CFT, extending understanding beyond neutral black holes.

Findings

Thermalization times are larger for charged black holes compared to Schwarzschild-AdS black holes.

Increasing black hole charge leads to longer thermalization times.

The behavior of probes is consistent across different chemical potential values.

Abstract

The time-scale of thermalization in holographic dual models with a chemical potential in diverse number of dimensions is systematically investigated using the gauge/gravity duality. We consider a model with a thin-shell of charged dust collapsing from the boundary toward the bulk interior of asymptotically anti-de Sitter (AdS) spaces. In the outer region there is a Reissner-Nordstr\"om-AdS black hole (RNAdS-BH), while in the inner region there is an anti-de Sitter space. We consider renormalized geodesic lengths and minimal area surfaces as probes of thermalization, which in the dual quantum field theory (QFT) correspond to two-point functions and expectation values of Wilson loops, respectively. We show how the behavior of these extensive probes changes for charged black holes in comparison with Schwarzschild-AdS black holes (AdS-BH), for different values of the black hole mass and charge. The full range of values of the chemical potential over temperature ratio in the dual QFT is investigated. In all cases, the structure of the thermalization curves shares similar features with those obtained from the AdS-BH. On the other hand, there is an important difference in comparison with the AdS-BH: the thermalization times obtained from the renormalized geodesic lengths and the minimal area surfaces are larger for the RNAdS-BH, and they increase as the black hole charge increases.