Evading the Trans-Planckian problem with Vaidya spacetimes

TL;DR

This paper proposes a kinematic model using Vaidya spacetimes to address the trans-Planckian problem in Hawking radiation, suggesting that Hawking photons originate outside the horizon rather than from near it.

Contribution

It introduces a purely kinematical Vaidya spacetime model to better understand Hawking evaporation and the trans-Planckian issue, focusing on the shell's acceleration and its relation to Unruh temperature.

Findings

Explicit calculation of shell's 4-acceleration including gravity and flux effects

Relation between shell acceleration and Unruh temperature established

Model suggests Hawking photons originate outside the horizon

Abstract

Hawking radiation, when treated in the ray optics limit, exhibits the unfortunate trans-Planckian problem --- a Hawking photon near spatial infinity, if back-tracked to the immediate vicinity of the horizon is hugely blue-shifted and found to have had trans-Planckian energy. (And if back-tracked all the way to the horizon, the photon is formally infinitely blue-shifted, and formally acquires infinite energy.) Unruh has forcefully argued that this implies that the Hawking flux represents a vacuum instability in the presence of a horizon, and that the Hawking photons are actually emitted from some region exterior to the horizon. We seek to make this idea more precise and somewhat explicit by building a purely kinematical model for Hawking evaporation based on two Vaidya spacetimes (outer and inner) joined across a thin time-like boundary layer. The kinematics of this model is already quite rich, and we shall defer consideration of the dynamics for subsequent work. In particular we shall present an explicit calculation of the the 4-acceleration of the shell (including the effects of gravity, motion, and the outgoing null flux) and relate this 4-acceleration to the Unruh temperature.