Black hole radiation with high frequency dispersion

TL;DR

This paper analytically investigates how high frequency dispersion modifies the spectrum of black hole radiation, explaining deviations from the thermal Hawking spectrum observed in numerical studies.

Contribution

It provides an analytical derivation of high frequency deviations in black hole radiation spectrum due to dispersion effects, complementing previous numerical findings.

Findings

High frequency spectrum deviates from thermal distribution

Analytical form of deviation is derived

Qualitative explanation of numerical results

Abstract

We consider one model of a black hole radiation, in which the equation of motion of a matter field is modified to cut off high frequency modes. The spectrum in the model has already been analytically derived in low frequency range, which has resulted in the Planckian distributin of the Hawking temperature. On the other hand, it has been numerically shown that its spectrum deviates from the thermal one in high frequency range. In this paper, we analytically derive the form of the deviation in the high frequency range. Our result can qualitatively explain the nature of the numerically calculated spectrum. The origin of the deviation is clarified by a simple discussion.