Minimal conditions for the existence of a Hawking-like flux

TL;DR

This paper identifies the minimal conditions, specifically an exponential peeling relationship of null geodesics, necessary for a Hawking-like radiation flux to reach future null infinity without requiring horizon formation.

Contribution

It demonstrates that horizon formation is not necessary for Hawking-like flux, emphasizing the role of null geodesic peeling and adiabaticity in radiation emergence.

Findings

Hawking-like flux can occur without horizons.

Exponential peeling of null geodesics is essential.

Flux temperature can evolve over time.

Abstract

We investigate the minimal conditions that an asymptotically flat general relativistic spacetime must satisfy in order for a Hawking-like Planckian flux of particles to arrive at future null infinity. We demonstrate that there is no requirement that any sort of horizon form anywhere in the spacetime. We find that the irreducible core requirement is encoded in an approximately exponential "peeling" relationship between affine coordinates on past and future null infinity. As long as a suitable adiabaticity condition holds, then a Planck-distributed Hawking-like flux will arrive at future null infinity with temperature determined by the e-folding properties of the outgoing null geodesics. The temperature of the Hawking-like flux can slowly evolve as a function of time. We also show that the notion of "peeling" of null geodesics is distinct, and in general different, from the usual notion of "inaffinity" used in Hawking's definition of surface gravity.