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Bifurcation diagrams for spacetime singularities and black holes

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Cotsakis, Spiros 


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.


Acknowledgements: The author is especially grateful to Gary Gibbons for many useful discussions which have had a positive effect on the final manuscript. A Visiting Fellowship to Clare Hall, University of Cambridge, is gratefully acknowledged. The author further thanks Clare Hall for its warm hospitality and partial financial support. This research was funded by RUDN University, scientific project number FSSF-2023-0003.


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The European Physical Journal C

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Springer Berlin Heidelberg