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 $$\textbf{R}^{3,1}$$ R 3 , 1 to $$dS_{3}\times \textbf{R}$$ d S 3 × 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 $$\textbf{R}^{3,1}$$ R 3 , 1 , the holographic conformal field theory plasma can reach a state in which $$\varepsilon = P_T = - P_L$$ ε = P T = - P L , with $$\varepsilon $$ ε , $$P_T$$ P T and $$P_L$$ 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 $$\textbf{R}^{3,1}$$ 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 $$\textbf{R}^{3,1}$$ R 3 , 1 faster than any power as we go back to early proper time. Hydrodynamic behavior can appear in intermediate time.