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Future stability of self-gravitating dust balls in an expanding universe

Beheshti, S. ORCID: 0009-0000-2197-3109, Normann, M. ORCID: 0000-0001-9239-1165 & Valiente Kroon, J. A. (2022). Future stability of self-gravitating dust balls in an expanding universe. Physical Review D, 105(12), article number 124027. doi: 10.1103/physrevd.105.124027


We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or singularities. The resulting solution to the Einstein-λ-dust equations exists for an infinite amount of time in the asymptotic region of the spacetime. Furthermore, we find that if the density is small compared to the cosmological constant, then it is possible to construct Cosmological solutions to the Einstein constraint equations on a standard Cauchy hypersurface representing self-gravitating balls of dust. If, in addition, the density is assumed to be sufficiently small, then this initial data gives rise to a future geodesically complete solution to the Einstein-λ-dust equations admitting a smooth conformal extension at infinity which can be regarded as a perturbation of de Sitter spacetime. The main technical tools in this analysis are Friedrich’s conformal Einstein field equations for the Einstein-λ-dust written in terms of a gauge in which the flow lines of the dust are recast as conformal geodesics.

Publication Type: Article
Additional Information: © 2022 American Physical Society.
Publisher Keywords: Evolution of the Universe; General relativity; Gravitation; Large scale structure of the Universe
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology
School of Science & Technology > Mathematics
SWORD Depositor:
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