Establish causal geodesic completeness of the regular solutions

Establish whether the maximal extensions of the regular black-hole solutions in the extended Holst-type Poincaré gauge models are causally geodesically complete.

Background

The paper derives regular black-hole geometries whose curvature and torsion remain finite at the centre, including solutions with primary torsion hair and Hayward-like solutions with secondary torsion hair. The authors emphasize that finite central curvature does not automatically determine the global structure of the spacetime.

The unresolved issue concerns the maximal extension of these regular solutions and whether all causal geodesics can be extended indefinitely. Resolving it requires a global analysis of the spacetime extensions and geodesic behavior, rather than only local regularity or horizon-structure calculations.

References

A complementary question concerns the maximal extension of the regular solutions and whether the resulting space-times are causally geodesically complete, since a finite curvature in the central region does not by itself establish these global properties.

— Black holes with torsion hair in cubic Holst-type Poincaré gauge gravity: from singular to regular geometries  (2609.08641 - Bahamonde et al., 8 Sep 2026) in Section 7, Conclusions (\ref{sec:conclusions})