On non-disk geometry of r = 0 in Kerr-de Sitter and Kerr-Newman-de Sitter spacetimes

TL;DR

This paper calculates the Gaussian curvature of the r=0, t=const surface in Kerr-de Sitter and Kerr-Newman-de Sitter spacetimes, revealing it is not a disk and clarifying its geometry.

Contribution

It provides the first analytical expressions for the Gaussian curvature of the r=0 surface in these spacetimes, challenging previous assumptions about its shape.

Findings

The surface r=0 is not a disk in these spacetimes.

Analytical expressions for Gaussian curvature are derived.

The geometry of the surface is clarified for both solutions.

Abstract

Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.