Analytic black branes in Lifshitz-like backgrounds and thermalization

TL;DR

This paper constructs Lifshitz-Vaidya black brane solutions to model anisotropic thermalization in quark-gluon plasma, revealing directional dependence and universality in entanglement entropy behavior influenced by the dynamical exponent.

Contribution

It introduces a new Lifshitz-Vaidya geometry for arbitrary dynamical exponent and applies it to study anisotropic thermalization and entanglement entropy in holographic plasma models.

Findings

Thermalization is faster in the transversal direction than in the longitudinal.

Entanglement entropy exhibits universal features across subsystems.

Characteristics of the system depend strongly on the critical exponent .

Abstract

Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary dynamical exponent $\nu$, we construct the Vaidya geometry, asymptoting to the Lifshitz-like spacetime, which represents a thin shell infalling at the speed of light. We apply the new Lifshitz-Vaidya background to study the thermalization process of the quark-gluon plasma via the thin shell approach previously successfully used in several backgrounds. We find that the thermalization depends on the chosen direction because of the spatial anisotropy. The plasma thermalizes thus faster in the transversal direction than in the longitudinal one. To probe the system described by the Lifshitz-like backgrounds, we also calculate the holographic entanglement entropy for the subsystems delineated along both transversal and longitudinal directions. We show that the entropy has some universality in the behavior for both subsystems. At the same time, we find that certain characteristics strongly depend on the critical exponent $\nu$.