Self-Gravitating Bjorken Flow

TL;DR

This paper derives a self-gravitating solution to Einstein-fluid equations modeling Bjorken flow, revealing inhomogeneities and energy density corrections due to gravity in a relativistic hydrodynamics context.

Contribution

It provides the first exact solution incorporating full gravity effects into Bjorken flow, extending previous test hydrodynamics models.

Findings

Energy density acquires gravity-induced corrections in proper time.

Transverse energy density distribution becomes inhomogeneous, described by a hyperbolic cosine function.

Solution demonstrates how gravity influences relativistic fluid flow in high-energy physics.

Abstract

I present a solution to the full Einstein-fluid equations representing a self-gravitating Bjorken flow. The motion and the geometry become inhomogeneous in the plane transversal to the flow and the energy density profile acquires, due to gravity, corrections in terms of proper time as compared to the original test hydrodynamics. The transverse distribution of energy density, for example, becomes $\epsilon(\tau,r)/\epsilon(\tau,0)\,=\, \cosh^{-4}{(3ar)}$