Hawking temperature in the tunneling picture

TL;DR

This paper investigates the calculation of Hawking radiation via tunneling methods, revealing that using a canonical invariant approach yields twice the traditional Hawking temperature, challenging previous assumptions.

Contribution

It demonstrates that the tunneling probability should be computed using a canonical invariant integral, leading to a Hawking temperature twice the original value.

Findings

Using the invariant integral doubles the Hawking temperature.

The standard tunneling method may underestimate the Hawking temperature.

Canonical invariance is crucial in tunneling calculations.

Abstract

We examine Hawking radiation from a Schwarzschild black hole in several reference frames using the quasi-classical tunneling picture. It is shown that when one uses, $\Gamma \propto \exp(Im [\oint p dr])$, rather than, $\Gamma \propto \exp(2 Im [\int p dr])$, for the tunneling probability/decay rate one obtains twice the original Hawking temperature. The former expression for $\Gamma$ is argued to be correct since $\oint p dr$ is invariant under canonical transformations, while $\int p dr$ is not. Thus, either the tunneling methods of calculating Hawking radiation are suspect or the Hawking temperature is twice that originally calculated.