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General Relativity and Quantum Cosmology

arXiv:2111.15032 (gr-qc)
[Submitted on 30 Nov 2021 (v1), last revised 2 Sep 2022 (this version, v4)]

Title:Gravitational collapse of spherical shells of fluid in the isotropic homogeneous universe

Authors:Shuichi Yokoyama
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Abstract:We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and the de-Sitter Schwarzschild black hole one by the Gullstrand-Painlevé one. After determining the scale factor for a perfect fluid coexisting with cosmological constant, we determine the orbit of the collapsing shells of fluid from the continuity condition for density and the perpendicular component of pressure at interface. However the continuity condition cannot fix the orbit when there does not exist a perfect fluid inside the shells. In this case we determine the orbit from an equation of state for the fluid consisting a shell near the surface. Finally we confirm that the total energy defined in arXiv:2005.13233 is independent of the given time evolution in this system.
Comments: 1+22 pages, 6 figures, v2: clarification of the scale factor connecting to inflationary period, v3: further clarification, minor improvements, figures, references added, v4: reorganization, minor revisions, published version
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th)
Report number: YITP-21-142
Cite as: arXiv:2111.15032 [gr-qc]
  (or arXiv:2111.15032v4 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.2111.15032
Related DOI: https://doi.org/10.1016/j.physletb.2022.137418

Submission history

From: Shuichi Yokoyama [view email]
[v1] Tue, 30 Nov 2021 00:00:12 UTC (105 KB)
[v2] Tue, 14 Dec 2021 06:05:33 UTC (106 KB)
[v3] Fri, 6 May 2022 04:33:52 UTC (281 KB)
[v4] Fri, 2 Sep 2022 23:53:25 UTC (279 KB)
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