https://doi.org/10.1140/epjc/s10052-024-12388-3
Regular Article - Theoretical Physics
Bifurcation diagrams for spacetime singularities and black holes
1
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom
2
Clare Hall, University of Cambridge, Herschel Road, Cambridge CB3 9AL, United Kingdom
3
Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia
Received:
1
December
2023
Accepted:
27
December
2023
Published online:
14
January
2024
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.
© The Author(s) 2024
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