How Gubser flow ends in a holographic conformal theory

Abstract

Gubser flow is an axis-symmetric and boost-invariant evolution in a relativistic quantum field theory which is best studied by mapping ${\mathbf{R}}^{3,1}$ to $d{S}_3\times \mathbf{R}$ when the field theory has conformal symmetry. We show that at late de-Sitter time, which corresponds to large proper time and central region of the future wedge within ${\mathbf{R}}^{3,1}$, the holographic conformal field theory plasma can reach a state in which $\epsilon =P_T=-P_L$, with $\epsilon$, $P_T$ and $P_L$ being the energy density, transverse and longitudinal pressures, respectively. We further determine the full sub-leading behaviour of the energy-momentum tensor at late time. Restricting to flows in which the energy density decays at large transverse distance from the central axis in ${\mathbf{R}}^{3,1}$, we show that this decay should be faster than any power law. Furthermore, in this case the energy density also vanishes in ${\mathbf{R}}^{3,1}$ faster than any power as we go back to early proper time. Hydrodynamic behavior can appear in intermediate time.

Comments: 25 pages, 2 figures; version accepted in EPJ-C, Section 5 and concluding sections revised