Sparsity of Hawking Radiation in $D+1$ Space-Time Dimensions Including Particle Masses

TL;DR

This paper introduces a measure called 'sparsity' to characterize Hawking radiation's low density of states, extends it to higher dimensions and massive particles, and compares it with traditional black body radiation.

Contribution

It presents the first closed-form expressions for sparsity including particle masses in higher-dimensional black holes and demonstrates how this method aligns with known Hawking radiation results.

Findings

Sparsity effectively captures Hawking radiation's low density of states.

Closed-form sparsity expressions for massive particles in higher dimensions are derived.

Different particle spins contribute distinctly to the total Hawking radiation.

Abstract

Hawking radiation from an evaporating black hole has often been compared to black body radiation. However, this comparison misses an important feature of Hawking radiation: Its low density of states. This can be captured in an easy to calculate, heuristic, and semi-analytic measure called "sparsity". In this letter we shall present both the concept of sparsities and its application to $D+1$-dimensional Tangherlini black holes and their evaporation. In particular, we shall also publish for the first time sparsity expressions taking into account in closed form effects of non-zero particle mass. We will also see how this comparatively simple method reproduces results of (massless) Hawking radiation in higher dimensions and how different spins contribute to the total radiation in this context.