Geodesic incompleteness of some popular regular black holes

Throughout the study of the geodesics of some popular spherically symmetric regular black holes, we hereby prove that the analytically extended Hayward black hole is geodetically incomplete. The simplest extension of the Culetu-Simpson-Visser's non-analytic smooth black hole is also geodetically incomplete, with the exception of the antipodal continuation of the radial geodesics. However, the huge ambiguity in the extension of nonanalytic spacetimes is tantamount of geodesic incompleteness and such spacetimes do not solve the singularity issue unless at least all the extensions turn out to be complete. Hence, we provide several mere modifications of such spacetimes in order to make them geodetically complete in all possible extensions beyond r = 0.

Automated summary

Through the study of popular spherically symmetric regular black holes, we have proven that the analytically extended Hayward black hole and the simplest extension of the Culetu-Simpson-Visser's non-analytic smooth black hole are both geodetically incomplete. The huge ambiguity in the extension of nonanalytic spacetimes leads to geodesic incompleteness, and unless all extensions are complete, these spacetimes do not solve the singularity issue. Therefore, we propose several modifications to make these spacetimes geodetically complete in all possible extensions beyond r = 0.