An analytic model for gravitational collapse of spherical matter under mixed pressure

Abstract

We investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state for the matter near interface, where pressure constituted of the transverse component and the longitudinal one is proportional to energy density. We present analytic solutions for the equation of state and discuss parameter region to satisfy physical conditions such as the absence of the shell crossing singularity, the monotonic increase of the emergent infinite redshift surface and energy conditions. We finally show that adopting the definition presented in arXiv:2005.13233 the total energy in this time-dependent system is invariant under the given time evolution.

arXiv comment17 pages, 5 figures, v2: The continuity condition imposed at interface, the equation of state imposed near interface, more explanations and discussions, other minor modifications, v3: 21 pages, 9 figures, discussion of energy conditions, figures improved, published version

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Cited by in corpus (2)

• Conserved non-Noether charge in general relativity: Physical definition vs. Noether's 2nd theorem
• Gravitational collapse of spherical shells of fluid in the isotropic homogeneous universe