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Generalized Lemaitre-Tolman-Bondi Solutions with Pressure

Paul Lasky·Anthony Lun
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Abstract

Utilizing the ADM equations, we derive a metric and reduced field equations describing a general, spherically symmetric perfect fluid. The metric describes both the interior perfect fluid region and exterior vacuum Schwarzschild spacetime in a single coordinate patch. The exterior spacetime is in generalized Painleve-Gullstrand coordinates which is an infinite class of coordinate systems. In the static limit the system reduces to a Tolman-Oppenheimer-Volkoff equation on the interior with the exterior in Schwarzschild coordinates. We show the coordinate transformation for the non-static cases to comoving coordinates, where the metric is seen to be a direct generalization of the Lemaitre-Tolman-Bondi spacetime to include pressures.

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Paul Lasky, Anthony Lun. 2006-09-21. Generalized Lemaitre-Tolman-Bondi Solutions with Pressure. https://doi.org/10.1103/physrevd.74.084013

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