Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

TL;DR

This paper analyzes slice-stretching effects at the event horizon of Schwarzschild black holes during geodesic slicing with excision, revealing that slice stretching is not solely due to singularity avoidance.

Contribution

It provides a detailed analysis of slice-stretching phenomena at the event horizon in specific coordinate systems, challenging previous assumptions about their causes.

Findings

Outward movement of the event horizon ('slice sucking') observed.

Unbounded growth of the radial metric component ('slice wrapping') analyzed.

Late time behavior similar to maximal slicing found.

Abstract

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.