Analytic black branes in Lifshitz-like backgrounds and thermalization

Abstract

Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary dynamical exponent ν, 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 ν.

Multiplicity and theremalization time in heavy-ions collisions

“…There is a problem with action (6) since up to now we do not know the blacking version of the metric (5) as a solution to the model (6). However there is a possibility to support the metric (5) by another action and to find the corresponding blacking solution [32]. This action has the form…”

“…See Appendix in [32] for details. If the dilaton is constant and the Maxwell field vanishes, the metric (8) with ν = 1 turns out to be the black brane solution in the AdS background:…”

“…We can consider the thermalization time t therm of several physical quantities, for example the twopoint correlation functions, Wilson loops or the entanglement entropy [31][32][33]. All these quantities we can find in the holographically within geodesics approximations.…”

Holographic Wilson loops in anisotropic quark-gluon plasma.

“…This is the case of special interest for us. Vaidya solutions in these Lifshitz-like spacetimes have been found in [8]. The thermalization time of the 2-point correlators and the thermalization of the holographic entanglement entropy have been estimated in [7,8].…”

“…A non-zero temperature generalization of the Lifshitz-like spacetime (1) is a black brane background with the metric [8] …”