4D and 2D Evaporating Dilatonic Black Holes

TL;DR

This paper investigates the relationship between 4D and 2D models of evaporating dilatonic black holes, revealing that classical and semi-classical effects cause significant differences, especially near the end of evaporation.

Contribution

It provides a detailed analysis of how 4D and 2D descriptions of evaporating dilatonic black holes relate, highlighting the limitations of 2D models in capturing 4D dynamics.

Findings

4D Hawking radiation matches 2D in the throat region initially

Back-reaction limits the validity of 4D-2D matching during evaporation

Breakdown of the 4D solution occurs before apparent horizon formation

Abstract

The picture of S-wave scatering from a 4D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. In the "throat region" the r-t geometry is exactly that of a collapsing 2D black hole. The 4D Hawking radiation (in this classical background) gives the 2D Hawking radiation exactly in the throat region. Inclusion of the back-reaction changes this picture: the 4D solution can then be matched to the 2D one only if the Hawking radiation is very small and only at the beginning of the radiation. We give that 4D solution. When the total radiating energy approaches the energy carried by the shock wave, the 4D picture breaks down. This happens even before an apparent horizon is formed, which suggests that the 4D semi-classical solution is quite different from the 2D one.