  Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of
gravity, black holes may have discrete emission spectra. Using the time-energy
uncertainty principle they have also shown that, for a (non-rotating)
Schwarzschild black hole, the natural broadening $\delta\omega$ of the
black-hole emission lines is expected to be small on the scale set by the
characteristic frequency spacing $\Delta\omega$ of the spectral lines:
$\zeta^{\text{Sch}}\equiv\delta\omega/\Delta\omega\ll1$. BM have therefore
concluded that the expected discrete emission lines of the quantized
Schwarzschild black hole are unlikely to overlap. In this paper we calculate
the characteristic dimensionless ratio $\zeta(\bar
a)\equiv\delta\omega/\Delta\omega$ for the predicted BM emission spectra of
rapidly-rotating Kerr black holes (here $\bar a\equiv J/M^2$ is the
dimensionless angular momentum of the black hole). It is shown that $\zeta(\bar
a)$ is an increasing function of the black-hole angular momentum. In
particular, we find that the quantum emission lines of Kerr black holes in the
regime $\bar a\gtrsim 0.9$ are characterized by the dimensionless ratio
$\zeta(\bar a)\gtrsim1$ and are therefore effectively blended together. Our
results thus suggest that, even if the underlying mass (energy) spectrum of
these rapidly-rotating Kerr black holes is fundamentally discrete as suggested
by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with
the time-energy uncertainty principle) is expected to smear the black-hole
radiation spectrum into a continuum.
