On the origin of the particles in black hole evaporation

TL;DR

This paper analytically derives Hawking radiation considering arbitrary dispersion relations, revealing that it is primarily a low-energy phenomenon but can be affected by ultra-high energy deviations, impacting models of quantum gravity.

Contribution

It provides a general analytic derivation of Hawking radiation for arbitrary dispersion relations, highlighting the role of group and phase velocities at different energy scales.

Findings

Hawking temperature depends on group and phase velocities at the radiation frequency.

Hawking radiation is mainly a low-energy phenomenon.

Ultra-high energy deviations can lead to an ultraviolet catastrophe.

Abstract

We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $\omega(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $d\omega/dk$ and phase $\omega/k$ velocities evaluated at the frequency $\omega$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe'') and hence should not be a realistic model for the microscopic structure of quantum gravity.