The Hawking cascades of gravitons from higher-dimensional Schwarzschild black holes

TL;DR

This paper investigates how the Hawking radiation of gravitons from higher-dimensional Schwarzschild black holes differs from the 4D case, revealing that for dimensions greater than about 10, the emission becomes continuous rather than sparse.

Contribution

It demonstrates that the ratio of time gap to emission time decreases with increasing dimension, showing higher-dimensional black holes emit Hawking radiation more continuously.

Findings

For D ≥ 10, η(D) < 1, indicating continuous emission.

Hawking graviton emission becomes less sparse as dimension increases.

The emission process transitions from sparse to continuous in higher dimensions.

Abstract

It has recently been shown that the Hawking evaporation process of $(3+1)$-dimensional Schwarzschild black holes is characterized by the dimensionless ratio $\eta\equiv\tau_{\text{gap}}/\tau_{\text{emission}}\gg1$, where $\tau_{\text{gap}}$ is the characteristic time gap between the emissions of successive Hawking quanta and $\tau_{\text{emission}}$ is the characteristic timescale required for an individual Hawking quantum to be emitted from the Schwarzschild black hole. This strong inequality implies that the Hawking cascade of gravitons from a $(3+1)$-dimensional Schwarzschild black hole is extremely {\it sparse}. In the present paper we explore the semi-classical Hawking evaporation rates of {\it higher}-dimensional Schwarzschild black holes. We find that the dimensionless ratio $\eta(D)\equiv{{\tau_{\text{gap}}}/{\tau_{\text{emission}}}}$, which characterizes the Hawking emission of gravitons from the $(D+1)$-dimensional Schwarzschild black holes, is a {\it decreasing} function of the spacetime dimension. In particular, we show that higher-dimensional Schwarzschild black holes with $D\gtrsim 10$ are characterized by the relation $\eta(D)<1$. Our results thus imply that, contrary to the $(3+1)$-dimensional case, the characteristic Hawking cascades of gravitons from these higher-dimensional black holes have a {\it continuous} character.