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The aim is to analyze curvature-threshold conditions in rotating black hole geometries, moving beyond spherical symmetry.

July 1, 2026Open Access

Curvature-Threshold Surfaces in Rotating Black Hole Geometry

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The aim is to analyze curvature-threshold conditions in rotating black hole geometries, moving beyond spherical symmetry.
Examining the Kerr geometry as a stationary axisymmetric vacuum black hole background.
Constructing invariant curvature diagnostics using scalar and pseudoscalar curvature invariants.
Identifying threshold surfaces based on curvature invariants and their dependence on mass and angular momentum.
Established that the curvature threshold does not correspond to a single transition radius in rotating geometries.
Defined a family of threshold surfaces that vary with mass, rotation parameter, and polar angle.
Highlighted the necessity of accounting for angular structure in regularizing rotating black holes.

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Extends curvature-threshold conditions to rotating black holes, indicating new geometric structures.

Paruzel et al. (2026) studied this question.

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