Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes
An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the...
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2025-06-01
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| author | John W. Moffat |
| author_facet | John W. Moffat |
| author_sort | John W. Moffat |
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| description | An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original solution. A new regularized radial coordinate is introduced, leading to a singularity-free description of black hole interiors. Crucially, we demonstrate how this complex extension resolves the long-standing paradox of event horizon formation occurring only in the infinite future of distant observers. By analyzing trajectories in complex spacetime, we show that the horizon can form in finite complex time, reconciling the apparent contradiction between proper and coordinate time descriptions. This approach also provides a framework for the analytic continuation of information across event horizons, resolving the Hawking information paradox. We explore the physical interpretation of the complex extension versus its projection onto real spacetime. The gravitational collapse of a dust sphere with negligible dust is explored in the complex spacetime extension. The approach offers a mathematically rigorous framework for exploring quantum gravity effects within the context of classical general relativity. |
| format | Article |
| id | doaj-art-000935b5d873428da38d9a67dca38c74 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-000935b5d873428da38d9a67dca38c742025-08-20T03:32:27ZengMDPI AGAxioms2075-16802025-06-0114644010.3390/axioms14060440Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole ParadoxesJohn W. Moffat0Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, CanadaAn approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original solution. A new regularized radial coordinate is introduced, leading to a singularity-free description of black hole interiors. Crucially, we demonstrate how this complex extension resolves the long-standing paradox of event horizon formation occurring only in the infinite future of distant observers. By analyzing trajectories in complex spacetime, we show that the horizon can form in finite complex time, reconciling the apparent contradiction between proper and coordinate time descriptions. This approach also provides a framework for the analytic continuation of information across event horizons, resolving the Hawking information paradox. We explore the physical interpretation of the complex extension versus its projection onto real spacetime. The gravitational collapse of a dust sphere with negligible dust is explored in the complex spacetime extension. The approach offers a mathematically rigorous framework for exploring quantum gravity effects within the context of classical general relativity.https://www.mdpi.com/2075-1680/14/6/440complex variablesblack holesastrophysics |
| spellingShingle | John W. Moffat Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes Axioms complex variables black holes astrophysics |
| title | Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes |
| title_full | Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes |
| title_fullStr | Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes |
| title_full_unstemmed | Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes |
| title_short | Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes |
| title_sort | complex riemannian spacetime removal of black hole singularities and black hole paradoxes |
| topic | complex variables black holes astrophysics |
| url | https://www.mdpi.com/2075-1680/14/6/440 |
| work_keys_str_mv | AT johnwmoffat complexriemannianspacetimeremovalofblackholesingularitiesandblackholeparadoxes |