Self-Gravitating Relativistic Fluids: The Formation of a Free Phase Boundary in the Phase Transition from Hard to Soft

TL;DR

This paper proves the existence and uniqueness of a free phase boundary in a relativistic fluid model describing gravitational collapse, focusing on the phase transition from hard to soft and analyzing the local shock structure near null points.

Contribution

It establishes the existence and uniqueness of a free phase boundary in a relativistic fluid model with phase transition, including the local shock behavior near null points.

Findings

Proved existence of a free phase boundary.

Established uniqueness of the phase boundary.

Analyzed the local shock structure near null points.

Abstract

In the 1990's Christodoulou introduced an idealized fluid model intended to capture some of the features of the gravitational collapse of a massive star to form a neutron star or a black hole. This was the two-phase model introduced in 'Self-gravitating relativistic fluids: a two phase model', Arch. Rational Mech. Anal. 130, 343-400 (1995). The present work deals with the formation of a free phase boundary in the phase transition from hard to soft in this model. In this case the phase boundary has corners at the null points, the points which separate the timelike and spacelike components of the interface between the two phases. We prove existence and uniqueness of a free phase boundary. Also the local form of the shock near the null point is established.