What question did this study set out to answer?

To re-examine the two-sheeted topology of extended Kerr-type spacetimes and establish topological laws governing geodesics traversing the singular ring complement.

August 16, 2026Open Access

The Two-Sheeted Topology of Extended Kerr-Type Spacetimes and a Parity-of-Crossings Property for Ring-Traversing Geodesics

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To re-examine the two-sheeted topology of extended Kerr-type spacetimes and establish topological laws governing geodesics traversing the singular ring complement.
Analyzed the topological double cover of excised Kerr spacetimes using algebraic topology and fundamental groups.
Evaluated geodesic equations of motion across the regular r=0 disk using Carter constant constraints (Q < 0).
Classified connected double covers for N unlinked rings and extended the analysis to maximal subextreme Kerr extensions.
Demonstrated that causal geodesics smoothly crossing the regular r=0 disk flip the sign of radial coordinate r, obeying a mod-2 crossing parity law where even parity preserves and odd parity swaps the sheet label.
Established that event- and Cauchy-horizon crossings remain neutral with respect to sheet-label parity, and crossing the r=0 disk preserves standard time orientation.
Showed that identifying the restricted time-orientation cover with the uniform meridional cover restricts smooth closed timelike curves to even uniform crossing parity.

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Implication

Theoretical analysis reveals a mod-2 crossing parity rule for geodesics traversing the regular disk in extended Kerr spacetimes, indicating topological constraints on closed timelike curves.

Cite This Study

A 2026 study studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac2c9 https://doi.org/10.5281/zenodo.21934405

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Implication

Theoretical analysis reveals a mod-2 crossing parity rule for geodesics traversing the regular disk in extended Kerr spacetimes, indicating topological constraints on closed timelike curves.

The Two-Sheeted Topology of Extended Kerr-Type Spacetimes and a Parity-of-Crossings Property for Ring-Traversing Geodesics

Key Points

Discussion

Implication

Cite This Study

The Two-Sheeted Topology of Extended Kerr-Type Spacetimes and a Parity-of-Crossings Property for Ring-Traversing Geodesics

Key Points

Discussion

Implication

Cite This Study

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