An exact spherically symmetric analytic collapse model grows an apparent horizon H(t) from zero to 2M while hiding an integrable central singularity and preserving weak cosmic censorship without exotic matter.
Generalized Lemaitre-Tolman-Bondi Solutions with Pressure
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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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gr-qc 1years
2026 1verdicts
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An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole
An exact spherically symmetric analytic collapse model grows an apparent horizon H(t) from zero to 2M while hiding an integrable central singularity and preserving weak cosmic censorship without exotic matter.