Self-similar collapse in Painlevé–Gullstrand coordinates

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 th...

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Bibliographic Details
Published inThe European physical journal. C, Particles and fields Vol. 84; no. 6; pp. 600 - 10
Main Authors Chakrabarti, Soumya, Singha, Chiranjeeb
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 10.06.2024
Springer Nature B.V
SpringerOpen
Subjects
Astronomy
Astrophysics and Cosmology
Black holes
Coordinates
Elementary Particles
Exact solutions
Flow velocity
Geometry
Gravitational collapse
Hadrons
Heavy Ions
Mathematical analysis
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Parameters
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Radiation
Regular Article – Theoretical Physics
Relativity
Schwarzschild metric
Self-similarity
String Theory
Symmetry
Tensors
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Summary: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.
ISSN:1434-6052
1434-6044
1434-6052
DOI:10.1140/epjc/s10052-024-12962-9