How Gubser flow ends in a holographic conformal theory

Gubser flow is an axis-symmetric and boost-invariant evolution in a relativistic quantum field theory which is best studied by mapping R3,1 R 3 , 1 to dS₃× 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 R3,1 R 3 , 1 , the holographic conformal field theory plasma can reach a state in which ε = PT = - PL ε = P T = - P L , with ε ε , PT P T and PL 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 R3,1 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 R3,1 R 3 , 1 faster than any power as we go back to early proper time. Hydrodynamic behavior can appear in intermediate time.