Weak null singularity for the Einstein-Euler system

2025/06/19 by Song, Yuefeng · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2506.16635

openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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Cited by

• Volume-Distance-Ratio Asymptote and Spacetime Inextendibility for FLRW Spacetimes
• Spacetime inextensibility criteria by volume-distance-ratio asymptote and applications to naked singularities and FLRW spacetimes

Related

• Weak null singularities in general relativity
• The breakdown of weak null singularities inside black holes
• The coexistence of null and spacelike singularities inside spherically symmetric black holes
• Naked singularities in the Einstein-Euler system
• Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity