  The quantum genesis of Hawking radiation is a long-standing puzzle in black
hole physics. Semi-classically one can argue that the spectrum of radiation
emitted by a black hole look very much sparse unlike what is expected from a
thermal object. It was demonstrated through a simple quantum model that a
quantum black hole will retain a discrete profile, at least in the weak energy
regime. However, it was suggested that this discreteness might be an artifact
of the simplicity of eigen-spectrum of the model considered. Different quantum
theories can, in principle, give rise to different complicated spectra and make
the radiation from black hole dense enough in transition lines, to make them
look continuous in profile. We show that such a hope from a geometry-quantized
black hole is not realized as long as large enough black holes are dubbed with
a classical mass area relation in any gravity theory ranging from GR,
Lanczos-Lovelock to f(R) gravity. We show that the smallest frequency of
emission from black hole in any quantum description, is bounded from below, to
be of the order of its inverse mass. That leaves the emission with only two
possibilities. It can either be non-thermal, or it can be thermal only with the
temperature being much larger than 1/M.
