at Google ScholarTitle data
Andréasson, Håkan ; Rein, Gerhard:
Oppenheimer–Snyder Type Collapse for a Collisionless Gas.
In: Communications in Mathematical Physics.
Vol. 406
(2025)
.
- 284.
ISSN 1432-0916
DOI: https://doi.org/10.1007/s00220-025-05463-7
Abstract in another language
In 1939, Oppenheimer and Snyder showed that the continued gravitational collapse of a self-gravitating matter distribution can result in the formation of a black hole, cf. Oppenheimer and Snyder (Phys Rev 56:455–459, 1939). In this paper, which has greatly influenced the evolution of ideas around the concept of a black hole, matter was modeled as dust, a fluid with pressure equal to zero. We prove that when the corresponding initial data are suitably approximated by data for a collisionless gas as modeled by the Vlasov equation, then a trapped surface forms before the corresponding solution to the Einstein–Vlasov system can develop a singularity and again a black hole arises. As opposed to the dust case the pressure does not vanish for such solutions. As a necessary starting point for the analysis, which is carried out in Painlevé–Gullstrand coordinates, we prove a local existence and uniqueness theorem for regular solutions together with a corresponding extension criterion. The latter result will also become useful when one perturbs dust solutions containing naked singularities in the Vlasov framework.
Further data
| Item Type: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | gravitational collapse; Oppenheimer-Snyder solution; collisionless gas; Einstein-Vlasov system |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics > Professor Applied Mathematics - Univ.-Prof. Dr. Gerhard Rein Profile Fields > Advanced Fields > Nonlinear Dynamics |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 07 Oct 2025 05:35 |
| Last Modified: | 07 Oct 2025 05:35 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/94845 |