Sensitivity of Hawking radiation to superluminal dispersion relations

13 pages, 7 figures.-- PACS nrs.: 04.70.Dy; 04.60.Bc; 04.62.+v.-- ArXiv pre-print available at: http://arxiv.org/abs/0807.4147We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up.Financial support was provided by the Spanish MEC through the projects FIS2005-05736-C03-01, FIS2005-05736-C03-02, and FIS2006-26387-E.Peer reviewe