A note on future complete spacetimes with massless outgoing particles

Fajman, David; Schaman, Christoph

doi:10.1088/1361-6382/aa627e

Cited by 1 publication

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References 12 publications

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“…Cǫ. (9.14) 17 It is only near the light cone that certain null components of the metric enjoy improved decay estimates.…”

Section: Bootstrap Assumptionsmentioning

confidence: 99%

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

Bigorgne,

Fajman,

Joudioux

et al. 2020

Preprint

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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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“…Cǫ. (9.14) 17 It is only near the light cone that certain null components of the metric enjoy improved decay estimates.…”

Section: Bootstrap Assumptionsmentioning

confidence: 99%

“…For a global existence result in spherical symmetry without necessarily small (but strongly outgoing) initial data cf. [17]. Note that, for initial data 1 On the other hand, shock formation can be avoided in the presence of accelerated expansion [36,32,35,18].…”

mentioning

confidence: 99%

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

Bigorgne,

Fajman,

Joudioux

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

A note on future complete spacetimes with massless outgoing particles

Cited by 1 publication

References 12 publications

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

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

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