2024/04/29 by Soumya Chakrabarti, Chakrabarti, Soumya, Chiranjeeb Singha +1 · 1 citation
Earth and Planetary Sciences · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2404.18431
openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.