Strong Shock in the Uniformly Expanding Universe with a Spherical Void

TL;DR

This paper investigates the behavior of strong shock waves in an expanding universe with a spherical void, analyzing how different adiabatic indices affect the shock structure through analytic and numerical methods.

Contribution

It provides a comparative analysis of approximate analytic and exact numerical solutions for shock propagation in an expanding universe, highlighting the effects of the adiabatic index on void formation.

Findings

For $1<b3<b3_{cr}a0a0 solutions fill all space without voids.

For $b3>b3_{cr}$, a spherical void appears around the origin.

At $b3 \u2265 1.4$, the density jumps from zero to infinity at the inner edge of the matter layer.

Abstract

Propagation of strong shock wave in the expanding universe is studied using approximate analytic, and exact numerical solution of self-similar equations. Both solutions have similar properties, which change qualitatively, depending on the adiabatic powers $\gamma$. In the interval $1<\gamma<\gamma_{cr} \sim 1.16$ analytic and numeric solutions fill all the space without any voids and they are rather close to each other. At larger $\gamma>\gamma_{cr}$ a pressure becomes zero at finite radius, and a spherical void appears around the origin in both solutions. All matter is collected in thin layer behind the shock wave front. The structure of this layer qualitatively depends on $\gamma$. At the inner edge of the layer the pressure is always zero, but the density on this edge is jumping from zero to infinity at $\gamma \approx 1.4$ in both solutions.