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

It has recently been shown that the Hawking evaporation process of (3+1)(3+1)-dimensional Schwarzschild black holes is characterized by the dimensionless ratio η≡τgap/τemission≫1η≡τgap/τemission≫1, where τgapτgap is the characteristic time gap between the emissions of successive Hawking quanta and τemissionτemission 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)(3+1)-dimensional Schwarzschild black hole is extremely sparse. In the present paper we explore the semi-classical Hawking evaporation rates of higher  -dimensional Schwarzschild black holes. We find that the dimensionless ratio η(D)≡τgap/τemissionη(D)≡τgap/τemission, which characterizes the Hawking emission of gravitons from the (D+1)(D+1)-dimensional Schwarzschild black holes, is a decreasing   function of the spacetime dimension. In particular, we show that higher-dimensional Schwarzschild black holes with D≳10D≳10 are characterized by the relation η(D)<1η(D)<1. Our results thus imply that, contrary to the (3+1)(3+1)-dimensional case, the characteristic Hawking cascades of gravitons from these higher-dimensional black holes have a continuous character.