Two-dimensional semiclassical static black holes: Finite-mass correction to the Hawking temperature and outflux

TL;DR

This paper investigates how semiclassical backreaction effects modify the Hawking temperature and outflux of two-dimensional static black holes, revealing mass-dependent corrections that vanish at large mass.

Contribution

It provides the first analytical and numerical analysis of the leading-order mass correction to Hawking temperature and outflux in 2D black holes.

Findings

Backreaction introduces a 1/M correction to temperature and outflux.

Analytical calculations match numerical integrations.

Corrections diminish as black hole mass increases.

Abstract

In the two-dimensional framework, the surface gravity of a (classical) black hole is independent of its mass $M$. As a consequence, the Hawking temperature and outflux are also independent of $M$ at the large-$M$ limit. (This contrasts with the four-dimensional framework, in which the surface gravity and temperature scale as 1/M.) However, when the semiclassical backreaction effects on the black-hole geometry are taken into account, the surface gravity is no longer $M$-independent, and the same applies to the Hawking temperature and outflux. This effect, which vanishes at the large-$M$ limit, increases with decreasing $M$. Here we analyze the semiclassical field equations for a two-dimensional static black hole, and calculate the leading-order backreaction effect ($\propto 1/M$) on the Hawking temperature and outflux. We then confirm our analytical result by numerically integrating the semiclassical field equations.