https://doi.org/10.1140/epjc/s10052-024-12962-9
Regular Article – Theoretical Physics
Self-similar collapse in Painlevé–Gullstrand coordinates
1
Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Tiruvalam Rd, Katpadi, 632014, Vellore, Tamil Nadu, India
2
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, 411007, Pune, India
a
soumya.chakrabarti@vit.ac.in
Received:
6
May
2024
Accepted:
23
May
2024
Published online:
10
June
2024
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.
© The Author(s) 2024
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