Gauss-Bonnet Gravity and Spacetime Singularities
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arXiv
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| Format: | Preprint |
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2026
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| author | Allaithy, Tariq Awad, Adel Radwan, Mohamed Hany Zahran, Mohsen |
| author_facet | Allaithy, Tariq Awad, Adel Radwan, Mohamed Hany Zahran, Mohsen |
| contents | We investigate the effect of higher-order curvature terms, specifically Gauss-Bonnet terms, on spacetime singularities in five dimensions. For FLRW cosmologies, we demonstrate that Gauss-Bonnet terms can replace the Big Bang/Crunch with a "sudden" singularity, characterized by a finite scale factor and Hubble rate but diverging higher-order derivatives. Investigating various branches of solutions shows the possibility of explicit extension of non-spacelike geodesics beyond the singular point. Furthermore, we employ the Gauss-Bonnet junction conditions to verify the consistency of the extension with the field equations. The whole solution describes a contracting phase prior to the expansion phase with a well-defined surface stress-energy tensor. Regarding the Boulware-Deser black hole, we find that Gauss-Bonnet terms soften the central singularity for radial geodesics--rendering them "weak" according to the Tipler and Krolak criteria--whereas non-radial geodesics remain strongly singular. Junction condition analysis of this solution shows that although higher-curvature corrections alter the nature of the singularity, geodesics are still inextendible as a result of divergent extrinsic curvature. Our results are consistent with the Penrose-Hawking singularity theorems since in Gauss-Bonnet black holes, geodesics suffer from focusing (expansion parameter diverges), while in cosmology, there is no focusing since the expansion parameter remains finite at the singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19150 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gauss-Bonnet Gravity and Spacetime Singularities Allaithy, Tariq Awad, Adel Radwan, Mohamed Hany Zahran, Mohsen General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate the effect of higher-order curvature terms, specifically Gauss-Bonnet terms, on spacetime singularities in five dimensions. For FLRW cosmologies, we demonstrate that Gauss-Bonnet terms can replace the Big Bang/Crunch with a "sudden" singularity, characterized by a finite scale factor and Hubble rate but diverging higher-order derivatives. Investigating various branches of solutions shows the possibility of explicit extension of non-spacelike geodesics beyond the singular point. Furthermore, we employ the Gauss-Bonnet junction conditions to verify the consistency of the extension with the field equations. The whole solution describes a contracting phase prior to the expansion phase with a well-defined surface stress-energy tensor. Regarding the Boulware-Deser black hole, we find that Gauss-Bonnet terms soften the central singularity for radial geodesics--rendering them "weak" according to the Tipler and Krolak criteria--whereas non-radial geodesics remain strongly singular. Junction condition analysis of this solution shows that although higher-curvature corrections alter the nature of the singularity, geodesics are still inextendible as a result of divergent extrinsic curvature. Our results are consistent with the Penrose-Hawking singularity theorems since in Gauss-Bonnet black holes, geodesics suffer from focusing (expansion parameter diverges), while in cosmology, there is no focusing since the expansion parameter remains finite at the singularity. |
| title | Gauss-Bonnet Gravity and Spacetime Singularities |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.19150 |