# Regularity results for the spherically symmetric Einstein-Vlasov system - General Relativity and Quantum Cosmology

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Abstract: The spherically symmetric Einstein-Vlasov system is considered inSchwarzschild coordinates and in maximal-isotropic coordinates. An open problemis the issue of global existence for initial data without size restrictions.The main purpose of the present work is to propose a method of approach forgeneral initial data, which improves the regularity of the terms that need tobe estimated compared to previous methods. We prove that global existence holdsoutside the centre in both these coordinate systems. In the Schwarzschild casewe improve the bound on the momentum support obtained in \cite{RRS} for compactinitial data. The improvement implies that we can admit non-compact data withboth ingoing and outgoing matter. This extends one of the results in\cite{AR1}. In particular our method avoids the difficult task of treating thepointwise matter terms. Furthermore, we show that singularities never form inSchwarzschild time for ingoing matter as long as $3m\leq r.$ This removes anadditional assumption made in \cite{A1}. Our result in maximal-isotropiccoordinates is analogous to the result in \cite{R1}, but our method isdifferent and it improves the regularity of the terms that need to be estimatedfor proving global existence in general.

Autor: Hakan Andreasson

Fuente: https://arxiv.org/