Trans-Planckian Tail in a Theory with a Cutoff

TL;DR

This paper investigates how a cutoff scale affects trans-Planckian frequencies near black holes, showing that Hawking radiation can be preserved while modifying the perception of the horizon for different observers.

Contribution

It introduces a final state condition involving only sub-cutoff frequencies to reconcile trans-Planckian effects with Hawking radiation.

Findings

Hawking radiation is restored for static observers despite the cutoff.

Freely falling observers perceive empty space but experience heating at the horizon.

A new boundary condition is proposed at the singularity involving low-frequency modes.

Abstract

Trans-planckian frequencies can be mimicked outside a black-hole horizon as a tail of an exponentially large amplitude wave that is mostly hidden 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 singularity. Despite the introduction of the cutoff, the Hawking radiation is restored for static observers. Freely falling observers see empty space outside the horizon, but are "heated" as they cross the horizon.