Origin of the particles in black hole evaporation

We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation ω(k) as a model for ultrahigh-energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group dω/dk and phase ω/k velocities evaluated at the frequency ω 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 ultrashort distances would generate Hawking radiation at ultrahigh energies (“ultraviolet catastrophe”) and hence should not be a realistic model for the microscopic structure of quantum gravity.