The Einstein-Vlasov system in maximal areal coordinates---Local existence and continuation

Sebastian Günther; Gerhard Rein

doi:10.3934/krm.2021040

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2022, Volume 15, Issue 4: 681-719. Doi: 10.3934/krm.2021040

This issue Previous Article A second look at the Kurth solution in galactic dynamics Next Article On time decay for the spherically symmetric Vlasov-Poisson system

The Einstein-Vlasov system in maximal areal coordinates---Local existence and continuation

Sebastian Günther and
Gerhard Rein^,

Department of Mathematics, University of Bayreuth, Germany

^* Corresponding author: Gerhard Rein
^* Corresponding author: Gerhard Rein

Dedicated to the memory of Prof. Robert T. Glassey

Received: April 30, 2021

Published: August 2022

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Abstract

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in maximal areal coordinates. The latter coordinates have been used both in analytical and numerical investigations of the Einstein-Vlasov system [3,8,18,19], but neither a local existence theorem nor a suitable continuation criterion has so far been established for the corresponding nonlinear system of PDEs. We close this gap. Although the analysis follows lines similar to the corresponding result in Schwarzschild coordinates, essential new difficulties arise from to the much more complicated form which the field equations take, while at the same time it becomes easier to control the necessary, highest order derivatives of the solution. The latter observation may be useful in subsequent investigations.

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Mathematics Subject Classification: Primary: 35Q85, 35Q76; Secondary: 85A05.

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