Slices of the Kerr ergosurface

TL;DR

This paper characterizes the intrinsic geometry of the Kerr ergosurface on different time slices, revealing differences in singularities, embeddability, and geometric limits related to the spin parameter.

Contribution

It provides a detailed comparison of the geometry of Kerr ergosurfaces across various slices, highlighting novel properties of Doran slices and extremal limits.

Findings

Doran slices lack conical singularities at poles except in extremal limit

Finite polar circumference in the extremal limit for certain slices

Doran slice develops embeddable polar cap for spin > 0.96

Abstract

The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite polar circumference in the extremal limit, and (iii) for sufficiently large spin parameter fail to be isometrically embeddable as a surface of revolution above some latitude. The Doran slice develops an embeddable polar cap for spin parameters greater than about 0.96.