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#### Initial-boundary value problem for the spherically symmetric Einstein equations for a perfect fluid

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##### Citation

Kind, S., & Ehlers, J. (1993). Initial-boundary value problem for the spherically
symmetric Einstein equations for a perfect fluid.* Classical and Quantum Gravity,* *10*(10), 2123-2136. doi:10.1088/0264-9381/10/10/020.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5C2A-0

##### Abstract

It is shown that for a given spherically symmetric distribution of a perfect fluid on a spacelike hypersurface with a boundary and a given, time-dependent boundary pressure, there exists a unique, local-in-time solution of the Einstein equations. A Schwarzchild spacetime can be attached to the fluid body if and only if the boundary pressure vanishes. We assume a smooth equation of state for which the density and the speed of sound remain positive for vanishing pressure.