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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03934 |
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| _version_ | 1866910040466653184 |
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| author | Bahn, Sune Rastad Andersen, Michael Cramer |
| author_facet | Bahn, Sune Rastad Andersen, Michael Cramer |
| contents | This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring differentiability of the time component of the metric leads to a sign change across the horizon, violating the Principle of Equivalence locally. We find a solution within the event horizon with a simple ``cosmological constant'' stress-energy tensor. Considering the impact of sign change to a compact stellar remnant, modeled by an incompressible perfect fluid obeying the Tolman-Oppenheimer-Volkoff equation, we rediscover the same geometry, indicating both mathematical and physical feasibility of the model. We also find a new theoretical limit M/R=3/8, which is lower than the Buchdahl limit of M/R=4/9 for the density of a perfect fluid that will recede behind an event horizon. The equation of state is discussed, and we propose that the final state is described by a Higgs-like free scalar field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lorentzian-Euclidean singularity-free solutions to gravitational collapse Bahn, Sune Rastad Andersen, Michael Cramer General Relativity and Quantum Cosmology This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring differentiability of the time component of the metric leads to a sign change across the horizon, violating the Principle of Equivalence locally. We find a solution within the event horizon with a simple ``cosmological constant'' stress-energy tensor. Considering the impact of sign change to a compact stellar remnant, modeled by an incompressible perfect fluid obeying the Tolman-Oppenheimer-Volkoff equation, we rediscover the same geometry, indicating both mathematical and physical feasibility of the model. We also find a new theoretical limit M/R=3/8, which is lower than the Buchdahl limit of M/R=4/9 for the density of a perfect fluid that will recede behind an event horizon. The equation of state is discussed, and we propose that the final state is described by a Higgs-like free scalar field. |
| title | Lorentzian-Euclidean singularity-free solutions to gravitational collapse |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.03934 |