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Gubser flow is an axis-symmetric and boost-invariant evolution in a
relativistic quantum field theory, providing a model for the evolution of
matter produced in the wake of heavy-ion collisions. It is best studied by
mapping $\mathbf{R}^{3,1}$ to $dS_{3}\times \mathbf{R}$ when the field theory
has conformal symmetry. We show that at late de-Sitter time, which corresponds
to large proper time and central region in $\mathbf{R}^{3,1}$, the generic
behavior for a holographic conformal field theory is given by $\varepsilon =
P_T = - P_L$, with $\varepsilon$, $P_T$ and $P_L$ being the energy density,
transverse and longitudinal pressures, respectively. We also show that the
general late de-Sitter time expansion can systematically determine both the
Minkowksi early proper time behavior and the profile at large distance from the
beam axis at any Minkowski proper time. Particularly, $\varepsilon = P_T = -
P_L$ is also generically realized at early Minkowski proper time, and we can
determine the (non-generic) initial conditions which generate the Gubser flow
in $\mathbf{R}^{3,1}$ in the holographic theory. Hydrodynamic modes appear at
intermediate time.
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