What question did this study set out to answer?

To organize the mathematical data and junction conditions required for spacetime continuation across the regular disk bounded by the Kerr ring singularity.

August 16, 2026Open Access

Global Continuation Across the Kerr Ring: Axiom Sets, Junction Data, and Disk-Crossing Geodesics

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To organize the mathematical data and junction conditions required for spacetime continuation across the regular disk bounded by the Kerr ring singularity.
Applied Darmois–Israel junction conditions to assess normal-reflection gluing across the timelike disk world tube of positive-mass Kerr blocks.
Analyzed disk-crossing trajectories and affine parameter behavior using the Carter equations.
Proved that no smooth tangential identification preserving the first fundamental form provides a C^1 vacuum reflection matching across the disk.
Identified that transverse disk crossings require a negative Carter constant (Q < 0) along with polar admissibility, occurring across a finite affine parameter.
Established that excising the negative-r branch while treating the regular disk as a boundary causes timelike and null geodesic incompleteness.

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Implication

Theoretical analysis demonstrates junction conditions and geodesic incompleteness across the Kerr ring disk, indicating that truncating negative-mass regions disrupts spacetime completeness.

Cite This Study

Sabbir Rahman (2026) studied this question.

synapsesocial.com/papers/6a81791ff2fb91fc834ac489 https://doi.org/10.5281/zenodo.21533931

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Implication

Theoretical analysis demonstrates junction conditions and geodesic incompleteness across the Kerr ring disk, indicating that truncating negative-mass regions disrupts spacetime completeness.

Global Continuation Across the Kerr Ring: Axiom Sets, Junction Data, and Disk-Crossing Geodesics

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Discussion

Implication

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Global Continuation Across the Kerr Ring: Axiom Sets, Junction Data, and Disk-Crossing Geodesics

Key Points

Discussion

Implication

Cite This Study

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