TRANS-PLANCKIAN TAIL IN A THEORY WITH A CUTOFF

Trans-Planckian frequencies can be mimicked outside a black-hole horiz on as a tail of an exponentially large amplitude wave that is mostly h idden behind the horizon. The present proposal requires implementing a final state condition. This condition involves only frequencies below the cutoff scale. It may be interpreted as a condition on the singula rity. Despite the introduction of the cutoff, the Hawking radiation is restored for static observers. Freely falling observers see empty spa ce outside the horizon, but are ''heated'' as they cross the horizon.