HAWKING SPECTRUM AND HIGH-FREQUENCY DISPERSION

We study the spectrum of created particles in two-dimensional black ho le geometries for a linear, Hermitian scalar field satisfying a Lorent z noninvariant field equation with higher spatial derivative terms tha t are suppressed by powers of a fundamental momentum scale k(0). The p referred frame is the ''free-fall frame'' of the black hole. This mode l is a variation of Unruh's sonic black hole analogy. We find that the re are two qualitatively different types of particle production in thi s model: a thermal Hawking flux generated by ''mode conversion'' at th e black hole horizon, and a nonthermal spectrum generated via scatteri ng off the background into negative free-fall frequency modes. This se cond process has nothing to do with black holes and does not occur for the ordinary wave equation because such modes do not propagate outsid e the horizon with positive Killing frequency. The horizon component o f the radiation is astonishingly close to a perfect thermal spectrum: for the smoothest metric studied, with Hawking temperature T-H similar or equal to 0.0008k(0), agreement is of order (T-H/k(0))(3) at freque ncy omega=T-H, and agreement to order T-H/k(0) persists out to omega/T -H similar or equal to 45 where the thermal number flux is similar to 10(-20). The flux from scattering dominates at large omega and becomes many orders of magnitude larger than the horizon component for metric s with a ''kink,'' i.e., a region of high curvature localized on a sta tic world line outside the horizon. This nonthermal flux amounts to ro ughly 10% of the total luminosity for the kinkier metrics considered. The flur exhibits oscillations as a function of frequency which can be explained by interference between the various contributions to the fl ux.