We investigate the effect of higher-order curvature terms, specifically Gauss-Bonnet terms, on spacetime singularities in five dimensions. For Friedmann-Lemaître-Robertson-Walker 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 nonspacelike 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 Królak criteria—whereas nonradial geodesics remain strongly singular. A 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.

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• Alternative gravity theories
• Cosmology
• General relativity
• Gravity in dimensions other than four