Coordinates with Non-Singular Curvature for a Time Dependent Black Hole Horizon

TL;DR

This paper explores a coordinate system for time-dependent black holes that avoids singularities at the horizon, providing insights into black hole evaporation and horizon dynamics.

Contribution

It introduces a non-singular coordinate framework for evolving black holes, improving understanding of horizon behavior during evaporation.

Findings

Ricci scalar remains non-singular away from the origin.

Null geodesics are slightly displaced from the coordinate singularity during evaporation.

Coordinate singularity structure is significantly altered in diagonal metrics.

Abstract

A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the horizon are slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity.