Admissible parameter and global coordinate domains

Determine the complete admissible parameter and global coordinate domains for the generalized black-hole families constructed from the fully non-aligned Ovcharenko–Podolský Einstein–Maxwell solution.

Background

The paper constructs an eight-parameter class of generalized black holes in four-dimensional Einstein–Maxwell theory, including twisting and non-twisting sectors and a charge parameter qq that may satisfy q2<0q^2<0. The analysis imposes local conditions such as Lorentzian signature, positivity of metric functions, reality of coordinate shifts, and angular regularity, but does not assemble these restrictions into a complete characterization of the allowed parameter space and global coordinate domains.

A complete domain analysis is important for determining which algebraic branches correspond to real Lorentzian spacetimes and for distinguishing genuine black-hole regions, acceleration horizons, singularities, and admissible coordinate patches.

References

A complete determination of the admissible parameter and global coordinate domains is left for future work.

— Generalized Black holes with Fully Non-aligned Electromagnetic Fields  (2609.10332 - Furugori et al., 9 Sep 2026) in Section 1, Introduction; reiterated in Section 2, subsection “Solution with \(\hat c_{00}=1\) and \(\hat c_{11}=-2\)”

It remains to determine whether their solutions are represented by limits or alternative parametrizations of the families discussed here.

— Generalized Black holes with Fully Non-aligned Electromagnetic Fields  (2609.10332 - Furugori et al., 9 Sep 2026) in Section 10, Summary and discussion, paragraph “Exceptional sectors”