Coordinates with non-singular curvature for a time dependent black hole horizon

摘要

A naive introduction of a dependency of the mass of a black hole on the Schwarlschild time coordinate results in singular behavior of curvature invariants at the horizon, violation expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate alin 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 block hole is constructed to examine the evolution of the coordinate singularity.