Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime

Jabiri, Fatima Ezzahra

doi:10.48550/arxiv.2001.08645

Cited by 2 publications

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“…By relaxing the condition of a regular centre the case with a Schwarzschild black hole was considered in [21], where the existence of massive static shells of Vlasov matter surrounding a black hole was shown. A different method leading to a similar result was more recently given by Jabiri in [18]. For a fluid, the first result of a massive static shell surrounding a black hole was obtained in [15].…”

Section: Introductionmentioning

confidence: 88%

Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

Andréasson

2021

Preprint

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We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einsteinmatter system which surround a black hole. We also include a numerical investigation about the properties of the shells.

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Section: Introductionmentioning

confidence: 88%

Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

Andréasson

2021

Preprint

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“…In the case when the individual particles in the ensemble are massive this system models distributions of stars, galaxies or galaxy clusters and constitutes an accurate model for the large scale structure of spacetime. It admits a large variety of nontrivial static solutions [29,30,4,3,22] which are potential attractors other than Minkowski space.…”

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confidence: 99%

Asymptotic Stability of Minkowski Space-Time with non-compactly supported massless Vlasov matter

Bigorgne,

Fajman,

Joudioux

et al. 2020

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We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov field in space or the momentum variables are required. In fact, the initial decay in v is optimal. The present proof is based on vector field and weighted vector field techniques for Vlasov fields, as developed in previous work of Fajman, Joudioux, and Smulevici, and heavily relies on several structural properties of the massless Vlasov equation, similar to the null and weak null conditions. To deal with the weak decay rate of the metric, we propagate well-chosen hierarchized weighted energy norms which reflect the strong decay properties satisfied by the particle density far from the light cone. A particular analytical difficulty arises at top order, when we do not have access to improved pointwise decay estimates for certain metric components. This difficulty is resolved using a novel hierarchy in the massless Einstein-Vlasov system, which exploits the propagation of different growth rates for the energy norms of different metric components.

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Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime

Cited by 2 publications

References 0 publications

Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

Asymptotic Stability of Minkowski Space-Time with non-compactly supported massless Vlasov matter

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