Space-time toy model for Hawking radiation

TL;DR

This paper introduces a simplified space-time toy model combining Minkowski and Rindler metrics to analytically study black-hole evaporation and Hawking radiation, clarifying the roles of different vacuum states.

Contribution

It presents an exact analytic framework for modeling black-hole evaporation using a simplified space-time setup, aiding understanding of Hawking radiation mechanisms.

Findings

Exact solutions for two-point functions in various vacuum states

Clarification of the roles of different vacuum states in Hawking radiation

A simplified model that makes complex phenomena analytically tractable

Abstract

By gluing together two sections of flat space-time in different metric representations (with the Minkowski metric representing the region far away from the black hole and the Rindler metric modeling the vicinity of the horizon), we construct a simplified toy model for black-hole evaporation. The simple structure of this toy model allows us to construct exact analytic solutions for the two-point functions in the various vacuum states (Israel-Harte-Hawking, Unruh and Boulware states) in an easy way and thus helps to understand and disentangle the different ingredients for Hawking radiation better.