  We present an analytic derivation of Hawking radiation for an arbitrary
(spatial) dispersion relation $\omega(k)$ as a model for ultra-high energy
deviations from general covariance. It turns out that the Hawking temperature
is proportional to the product of the group $d\omega/dk$ and phase $\omega/k$
velocities evaluated at the frequency $\omega$ of the outgoing radiation far
away, which suggests that Hawking radiation is basically a low-energy
phenomenon. Nevertheless, a group velocity growing too fast at ultra-short
distances would generate Hawking radiation at ultra-high energies
(``ultra-violet catastrophe'') and hence should not be a realistic model for
the microscopic structure of quantum gravity.
