Particle energy and Hawking temperature

TL;DR

This paper demonstrates that using the correct particle energy definition in the tunneling approach yields the accurate Hawking temperature for Schwarzschild black holes across different coordinate systems.

Contribution

It introduces a new definition of particle energy that ensures consistent Hawking temperature calculations in various coordinate systems.

Findings

Correct energy definition restores the standard Hawking temperature.

Application to Kruskal-Szekers and Lemaitre coordinates confirms the method's validity.

Addresses discrepancies in previous tunneling approach results.

Abstract

Some authors have recently found that the tunneling approach gives a different Hawking temperature for a Schwarzschild black hole in a different coordinate system. In this paper, we find that to work out the Hawking temperature in a different coordinate system by the tunneling approach, we must use the correct definition of the energy of the radiating particles. By using a new definition of the particle energy, we obtain the correct Hawking temperature for a Schwarzschild black hole in two dynamic coordinate systems, the Kruskal-Szekers and dynamic Lemaitre coordinate systems.