Hawking radiation and ultraviolet regulators

Polchinski has argued that the prediction of Hawking radiation must be independent of the details of unknown high-energy physics because the calculation may be performed using "nice slices," for which the adiabatic theorem may be used. If this is so, then any calculation using a manifestly covariant—and so slice-independent—ultraviolet regularization must reproduce the standard Hawking result. We investigate the dependence of the Hawking radiation on such a short-distance regulator by calculating it using a Pauli-Villars regularization scheme. We find that the regulator scale $\Lambda$ only contributes to the Hawking flux by an amount that is exponentially small in the large variable $\frac{\Lambda }{T_H}\gg 1$, where $T_H$ is the Hawking temperature, in agreement with Polchinski's arguments. Using the techniques of effective Lagrangians, we demonstrate the robustness of our results. We also solve a technical puzzle concerning the relation between the short-distance singularities of the propagator and the Hawking effect.