Larson-Penston Self-similar Gravitational Collapse

TL;DR

This paper rigorously proves the existence of the Larson-Penston self-similar solution, which describes the gravitational collapse of an isothermal fluid under Newtonian gravity, originally discovered through numerical methods in 1969.

Contribution

The paper provides a rigorous mathematical proof for the existence of the Larson-Penston self-similar gravitational collapse solution.

Findings

Existence of Larson-Penston solution is mathematically established.

The solution describes collapse of isothermal fluid under Newtonian gravity.

Supports previous numerical findings with rigorous proof.

Abstract

Using numerical integration, in 1969 Penston [22] and Larson [17] independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $p=k\varrho$, $k>0$, and subject to Newtonian gravity. We rigorously prove the existence of such a Larson-Penston solution.