Short-distance contribution to the spectrum of Hawking radiation

TL;DR

This paper investigates the impact of ultrashort distances on Hawking radiation spectrum, finding that contributions from Planck-scale physics are negligible below certain high frequencies, thus confirming the robustness of Hawking radiation predictions.

Contribution

It provides a new estimation method for ultrashort distance contributions to Hawking radiation within semiclassical theory, highlighting the frequency threshold where quantum gravity effects may become significant.

Findings

Hawking radiation is robust up to 96 T_H for black holes of three solar masses.

Ultrashort distance contributions are negligible below specific high frequencies.

Significant deviations from semiclassical predictions may occur only above these frequencies.

Abstract

The Hawking effect can be rederived in terms of two-point functions and in such a way that it makes it possible to estimate, within the conventional semiclassical theory, the contribution of ultrashort distances to the Planckian spectrum. For Schwarzschild black holes of three solar masses the analysis shows that Hawking radiation is very robust up to frequencies of 96 T_H or 270 T_H for bosons and fermions, respectively. For primordial black holes (with masses around 10^{15} g) these frequencies turn out to be of order 52T_H and 142 T_H. Only at these frequencies and above do we find that the contribution of Planck distances is of order of the total spectrum itself. Below this scale, the contribution of ultrashort distances to the spectrum is negligible. This suggests that only above these frequencies could an underlying quantum theory of gravity potentially predict significant deviations from Hawking's semiclassical result.