The paper remarks that the global prolongation problem for axisymmetric Einstein-Euler metrics is open and views the matter-vacuum matching problem as an opposite-direction approach to the same issue.
Makino, On spherically symmetric solutions of the Einstein-Euler equa- tions, Kyoto J
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A Remark on the Matter-Vacuum Matching Problem for Axisymmetric Metrics Governed by the Einstein-Euler Equations
The paper remarks that the global prolongation problem for axisymmetric Einstein-Euler metrics is open and views the matter-vacuum matching problem as an opposite-direction approach to the same issue.