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The aim is to eliminate the singularity issue in the Kerr-Schild class black hole models by modifying the mass function.

July 15, 2026Open Access

A Minimal C3 Regularisation of the Kerr-Schild Class in the Negative Radial Domain

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The aim is to eliminate the singularity issue in the Kerr-Schild class black hole models by modifying the mass function.
Introduced a minimal modification to the mass function for the negative radial domain.
Performed explicit computation of the one-sided derivatives at r = 0.
Conducted direct symbolic computation of the Kretschmann scalar to confirm regularity.
Proved the modified mass function is C3 at r = 0 with a fourth-derivative discontinuity of 48M/l3P.
Confirmed finiteness of the Kretschmann scalar everywhere with core value K(0) = 96M2/l6P.
Agreed with the standard form for r ≥ 0 and matched the standard Kerr mass at large |r|.

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Randomized trial demonstrates a novel metric function achieves black hole regularity, suggesting new insights for singularity removal.

Melchizedek-Kairós (2026) studied this question.

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