On weak solutions in Einstein theory and beyond

2025/05/03 by Francesco Fazzini, Hassan Mehmood, Fazzini, Francesco +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #advanced mathematical theories

paper · doi:10.48550/arxiv.2505.01846

openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In spherical symmetry, gravitational collapse of dust may give rise to the so-called shell-crossing singularities, beyond which spacetime can be extended using weak solutions to the integrated version of the equations of motion. We argue that the paradigm of weak solutions is ill-suited for dynamical extension beyond shell crossings through shock waves because it is based implicitly on an assumption that turns out to be unphysical for the shock and leads to the unwanted prospect of shock waves of dust particles moving faster than light.

Citations

• Dust shell in effective loop quantum black hole model
• Quantum induced shock dynamics in gravitational collapse: insights from effective models and numerical frameworks
• Shock waves in classical dust collapse
• Non-uniqueness of the shockwave dynamics in effective loop quantum gravity
• Causal structure of nonhomogeneous dust collapse in effective loop quantum gravity
• Status of Birkhoff's theorem in polymerized semiclassical regime of Loop Quantum Gravity
• Nonsingular collapse of a spherical dust cloud
• Generalized analysis of a dust collapse in effective loop quantum gravity: fate of shocks and covariance
• Rainbow Oppenheimer-Snyder collapse and the entanglement entropy production
• Initial value formalism for dust collapse
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• On Continued Gravitational Contraction

Cited by

• Effective LQG-inspired dynamics of a thin shell and the fate of a collapsing star
• Dust shell in effective loop quantum black hole model

Related

• Shock waves in classical dust collapse
• Non-uniqueness of the shockwave dynamics in effective loop quantum gravity
• Gravitational collapse of thin shell of dust in shape dynamics
• Hawking radiation from a collapsing dust sphere and its back reaction at the event horizon -Weak value approach-
• Initial value formalism for dust collapse