On the origin of the particles in black hole evaporation

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.Comment: 4 pages RevTe

On the Universality of the Hawking Effect

Addressing the question of whether the Hawking effect depends on degrees of freedom at ultra-high (e.g., Planckian) energies/momenta, we propose three rather general conditions on these degrees of freedom under which the Hawking effect is reproduced to lowest order. As a generalization of Corley's results, we present a rather general model based on non-linear dispersion relations satisfying these conditions together with a derivation of the Hawking effect for that model. However, we also demonstrate counter-examples, which do not appear to be unphysical or artificial, displaying strong deviations from Hawking's result. Therefore, whether real black holes emit Hawking radiation remains an open question and could give non-trivial information about Planckian physics. PACS: 04.70.Dy, 04.62.+v, 04.60.-m, 04.20.Cv.Comment: 11 pages RevTeX, 6 figure