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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta =\pi /2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mo>=</mo> <mi>π</mi> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> constant (in Boyer–Lindquist coordinates) is missing (multiple copies of) the region <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(r&lt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, representable as a triangle in the usual conformal diagram style.</p>

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

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  • 发表日期：

    2026年7月21日

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  • M. A. H. MacCallum

摘要

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 \(\theta =\pi /2\) θ = π / 2 , \(\phi \) ϕ constant (in Boyer–Lindquist coordinates) is missing (multiple copies of) the region \(r<0\) r < 0 , representable as a triangle in the usual conformal diagram style.