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

Abstract

The region spaning 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 $\theta =\pi /2$, $\varphi$ constant (in Boyer-Lindquist coordinates) is missing (multiple copies of) the region $r<0$, representable as a triangle in the usual conformal diagram style.

Based on a talk given at the CarterFest in 2022. Submitted to General Relativity and Gravitation

References in corpus (5)

• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• Space-time diagrammatics
• Darboux diagonalization of the spatial 3-metric in Kerr spacetime
• On non-disk geometry of r = 0 in Kerr-de Sitter and Kerr-Newman-de Sitter spacetimes
• Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region