On the Hawking effect

TL;DR

This paper models gravitational collapse using Painlevé-Gullstrand-Lemaître coordinates, explicitly calculates the Hawking temperature in 1+1 dimensions, and discusses how different collapse dynamics affect black hole evaporation or anti-evaporation.

Contribution

It provides a detailed calculation of Hawking radiation in a general, smooth gravitational collapse scenario and explores the effects of collapse dynamics on black hole evaporation.

Findings

Explicit calculation of Hawking temperature in 1+1 dimensions

Collapse dynamics determine evaporation or anti-evaporation

Outline of generalization to 3+1 dimensions

Abstract

In terms of the Painlev{\'e}-Gullstrand-Lema{\^\i}tre coordinates a rather general scenario for the gravitational collapse of an object and the subsequent formation of a horizon is described by a manifestly $C^\infty$-metric. For a 1+1 dimensional model of the collapse the leading contributions to the Bogoliubov coefficients are calculated explicitely and the Hawking temperature is recovered. But depending on the particular dynamics of the collapse the final state represents either evaporation or anti-evaporation. The generalization of the calculation to 3+1 dimensions is outlined and possible implications are addressed. PACS-numbers: 04.70.Dy, 04.70.-s, 04.62.+v.