On Coordinate Singularities Induced by Trapping Horizons

TL;DR

This paper investigates coordinate singularities caused by trapping horizons in dynamic black hole spacetimes, clarifying their geometric nature and illustrating the phenomenon with an analytical model.

Contribution

It identifies and clarifies a new class of coordinate singularities induced by trapping horizons, distinct from known singularities, using geometric analysis and an analytical model.

Findings

Identified a new class of coordinate singularities linked to trapping horizons.

Clarified the geometric structure of these singularities using the Kodama vector field.

Illustrated the phenomenon with the evolving Ellis drainhole model.

Abstract

The trapping (or apparent) horizon serves as a key tool for tracing the complete evolution of black holes. We investigate a class of coordinate singularities induced by such trapping (or apparent) horizons in a spherically symmetric, dynamic spacetime, which are distinct from the well-known coordinate singularities associated with the Killing horizon. In particular, we clarify the geometric structure of this coordinate singularity by means of the Kodama vector field, thereby avoiding unphysical artifacts. We further employ the evolving Ellis drainhole as an analytical model to illustrate key details of this phenomenon.