Shock waves in Lifshitz-like spacetimes

Abstract

We construct shock waves for Lifshitz-like geometries in four-and fivedimensional effective theories as well as in D3-D7 and D4-D6 brane systems. The solutions to the domain wall profile equations are found. Further, the study makes a connection with the implications for the quark-gluon plasma formation in heavy-ion collisions. According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions. We calculate the areas of trapped surfaces in the geometry of two colliding Lifshitz domain walls. Our estimates show that for five-dimensional cases with certain values of the critical exponent the dependence of multiplicity on the energy of colliding ions is rather close to the experimental data M ∼ s 0.15 observed at RHIC and LHC.

Analytic black branes in Lifshitz-like backgrounds and thermalization

“…Solutions interpolating between Lifshitz-like (1.2) and AdS geometries were intensively studied in [26]- [32] within the context of applications to the anisotropic QGP. However, the results for multiplicities calculated using the background (1.2) in [24] do not fit the experimental data unlike the case of the metric (1.1).…”

“…However, if one performs the holographic estimations of multiplicities in Lifshitz-like spacetimes [22,23,25], one can fit the experimental data for certain values of the critical exponents [24]. In this paper, we consider following the 5-dimensional Lifshitz-like metric:…”

“…To reproduce this anisotropy from the gravity side, one of the possible backgrounds is the Lifshitz-like metric (1.1). It has been shown in [24] that for the wall-on-wall collision in the 5d Lifshitz-like background with the critical exponent ν = 4, the dependence of multiplicity on the energy is desirable, i.e. behaves as E 1/3 .…”

“…In [24] we considered a collision of two domain walls in the five-dimensional Lifshitz-like background…”

“…Note that (2.1) is equivalent to (1.1) via the change of coordinate z =r −ν and the rescaling (t, x, y 1 , y 2 ) → ν −1 (t, x, y 1 , y 2 ). In [24,25] the metric ansatz (2.1) was considered for a 5d model governed by the action…”