Bogoliubov Coefficients of 2D Charged Black Holes

TL;DR

This paper precisely computes the Hawking radiation spectrum and temperature for a 2D charged black hole in equilibrium using Bogoliubov coefficients, highlighting the extremal limit where radiation vanishes.

Contribution

It provides an exact calculation of Hawking radiation for 2D charged black holes in equilibrium, extending previous models by considering a preexisting black hole background.

Findings

Hawking temperature is derived explicitly for the 2D charged black hole.

The extremal limit results in zero temperature and radiation.

The method uses Bogoliubov coefficients for exact analysis.

Abstract

We exactly calculate the thermal distribution and temperature of Hawking radiation for a two-dimensional charged dilatonic black hole after it has settled down to an "equilibrium" state. The calculation is carried out using the Bogoliubov coefficients. The background of the process is furnished by a preexisting black hole and not by collapsing matter as considered by Giddings and Nelson for the case of a Schwarzschild black hole. Furthermore, the vanishing of the temperature and/or the Hawking radiation in the extremal case is obtained as a regular limit of the general case.