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Two discs and a missing triangle: the maximally extended Kerr black hole revisited

2026/06/30 by Malcolm A. H. MacCallum, M. A. H. MacCallum
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Relativity and Gravitational Theory #gr-qc

paper · pdf · doi:10.1007/s10714-026-03587-2

openalex publication_date 2026/07/01 · openalex created_date 2026/07/22 · openalex updated_date 2026/07/23

Abstract

Abstract The region spanning the ring singularity in the Kerr black hole solution is described here as two (flat) discs rather than one. From this viewpoint it follows that the usual depiction of the worldsheet θ =π /2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , φ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> constant (in Boyer–Lindquist coordinates) is missing (multiple copies of) the region rlt;0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , representable as a triangle in the usual conformal diagram style.

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