Bifurcation diagrams for spacetime singularities and black holes
Abstract We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully nonlinear and dispersive nature of the underlying equations...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-12388-3 |
| _version_ | 1797233353414410240 |
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| author | Spiros Cotsakis |
| author_facet | Spiros Cotsakis |
| author_sort | Spiros Cotsakis |
| collection | DOAJ |
| description | Abstract We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully nonlinear and dispersive nature of the underlying equations. We introduce and thoroughly explore the concept of versal unfolding (topological normal form) within the framework of the Newman–Penrose–Raychaudhuri system, the convergence-vorticity equations (notably the first and third Sachs optical equations), and the Oppenheimer–Snyder equation governing exactly spherical collapse. The findings lead to a novel dynamical depiction of spacetime singularities and black holes, exposing their continuous transformations into new topological configurations guided by the bifurcation diagrams associated with these problems. |
| first_indexed | 2024-03-08T12:34:48Z |
| format | Article |
| id | doaj.art-d181d7e57c0f4e9e88e6eb9cf546cf43 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T16:14:49Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-d181d7e57c0f4e9e88e6eb9cf546cf432024-03-31T11:33:16ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-01-0184113810.1140/epjc/s10052-024-12388-3Bifurcation diagrams for spacetime singularities and black holesSpiros Cotsakis0Department of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully nonlinear and dispersive nature of the underlying equations. We introduce and thoroughly explore the concept of versal unfolding (topological normal form) within the framework of the Newman–Penrose–Raychaudhuri system, the convergence-vorticity equations (notably the first and third Sachs optical equations), and the Oppenheimer–Snyder equation governing exactly spherical collapse. The findings lead to a novel dynamical depiction of spacetime singularities and black holes, exposing their continuous transformations into new topological configurations guided by the bifurcation diagrams associated with these problems.https://doi.org/10.1140/epjc/s10052-024-12388-3 |
| spellingShingle | Spiros Cotsakis Bifurcation diagrams for spacetime singularities and black holes European Physical Journal C: Particles and Fields |
| title | Bifurcation diagrams for spacetime singularities and black holes |
| title_full | Bifurcation diagrams for spacetime singularities and black holes |
| title_fullStr | Bifurcation diagrams for spacetime singularities and black holes |
| title_full_unstemmed | Bifurcation diagrams for spacetime singularities and black holes |
| title_short | Bifurcation diagrams for spacetime singularities and black holes |
| title_sort | bifurcation diagrams for spacetime singularities and black holes |
| url | https://doi.org/10.1140/epjc/s10052-024-12388-3 |
| work_keys_str_mv | AT spiroscotsakis bifurcationdiagramsforspacetimesingularitiesandblackholes |