Weak null singularity for the Einstein-Euler system

TL;DR

This paper demonstrates that weak null singularities, previously studied in vacuum spacetimes, also occur in the Einstein-Euler system with a relativistic fluid, with fluid variables extending continuously to the singularity.

Contribution

It extends the understanding of weak null singularities to the Einstein-Euler system, showing the persistence of such singularities with continuous fluid variables.

Findings

Weak null singularities exist in the Einstein-Euler system.

Fluid variables extend continuously to the singularity.

The speed of sound being less than light is crucial for fluid extension.

Abstract

We study the behavior of a self-gravitating perfect relativistic fluid satisfying the Einstein-Euler system in the presence of a weak null terminal spacetime singularity. This type of singularities is expected in the interior of generic dynamical black holes. In the vacuum case, weak null singularities have been constructed locally by Luk, where the metrics extend continuously to the singularities while the Christoffel symbols fail to be square integrable in any neighborhood of any point on the singular boundaries. We prove that this type of singularities persists in the presence of a self-gravitating fluid. Moreover, using the fact that the speed of sound is strictly less than the speed of light, we prove that the fluid variables also extend continuously to the singularity.