Particle creation via high frequency dispersion

Abstract

We investigate the particle creation caused by a nonlinear dispersion relation for a massless scalar field propagating on a background curved spacetime in two dimensions. The dispersion relation adopted agrees with the standard dispersion relation at long wavelengths but is modified at short wavelengths, the division being characterized by a new length scale ${1/k}_0$. We consider both spacetimes with and without a black hole. Those without contain instead a uniformly moving “bump.” The black hole cases considered have Hawking temperatures $T_H>k_0/100\mathrm{}$. We find that the particle creation arises in all cases from two effects: scattering and mode conversion. The latter was identified by Corley and Jacobson as the phenomenon responsible for the Hawking effect.