Following an intriguing heuristic argument of Bekenstein , many researches have suggested during the last four decades that quantized black holes may be characterized by discrete radiation spectra .
Bekenstein and Mukhanov ( BM ) have further argued that the emission spectra of quantized ( 3 + 1 ) -dimensional Schwarzschild black holes are expected to be sharp in the sense that the characteristic natural broadening \delta \omega of the black-hole radiation lines , as deduced from the quantum time-energy uncertainty principle , is expected to be much smaller than the characteristic frequency spacing \Delta \omega = O ( T _ { \text { BH } } / \hbar ) between adjacent black-hole quantum emission lines .
It is of considerable physical interest to test the general validity of the interesting conclusion reached by BM regarding the sharpness of the Schwarzschild black-hole quantum radiation spectra .
To this end , in the present paper we explore the physical properties of the expected radiation spectra of quantized ( D + 1 ) -dimensional Schwarzschild black holes .
In particular , we analyze the functional dependence of the characteristic dimensionless ratio \zeta ( D ) \equiv \delta \omega / \Delta \omega on the number D + 1 of spacetime dimensions .
Interestingly , it is proved that the dimensionless physical parameter \zeta ( D ) , which characterizes the sharpness of the black-hole quantum emission spectra , is an increasing function of D .
In particular , we prove that the quantum emission lines of ( D + 1 ) -dimensional Schwarzschild black holes in the regime D \gtrsim 10 are characterized by the dimensionless ratio \zeta ( D ) \gtrsim 1 and are therefore effectively blended together .
The results presented in this paper thus suggest that , even if the underlying energy spectra of quantized ( D + 1 ) -dimensional Schwarzschild black holes are fundamentally discrete , as argued by many authors , the quantum phenomenon of natural broadening is expected to smear the characteristic emission spectra of these higher-dimensional black holes into a continuum .