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arXiv · 2404.18431

Self-Similar Collapse in Painleve-Gullstrand Coordinates

Soumya Chakrabarti·Chiranjeeb Singha
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Abstract

We report a family of self-similar exact solutions in General Relativity. The solutions are found in a Painleve-Gullstrand coordinate system but can also be transformed smoothly into a diagonal form. The solutions represent a gravitational collapse leading to three possible outcomes, depending on the parameter space : (i) a collapse followed by a bounce and dispersal of the clustered matter distribution, (ii) a rapid collapse followed by a bounce and an eventual re-collapse, and (iii) a standard collapse leading to zero proper volume. Profiles of the energy conditions are studied for all of the scenarios, and it is noted that a bounce is usually associated with a violation of the Null Energy Condition. It is found that more than one null surfaces (apparent horizons) can develop during the collapse. We also discuss that for a general metric tensor having a conformal symmetry, some regions of the parameter space allows a formation of null throat, much like a wormhole. Matching the metric with a Schwarzschild metric in Painleve-Gullstrand form leads to the geodesic equation for a zero energy falling particle in the exterior.

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Soumya Chakrabarti, Chiranjeeb Singha. 2024-04-29. Self-Similar Collapse in Painleve-Gullstrand Coordinates. https://arxiv.org/abs/2404.18431

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