Cosmological and Black Hole Horizon Fluctuations

TL;DR

This paper investigates quantum-induced fluctuations of cosmological and black hole horizons, showing that cosmological fluctuations are around the Planck scale, while black hole fluctuations are smaller for large black holes, supporting the semiclassical Hawking radiation theory.

Contribution

It introduces a model for horizon fluctuations caused by quantum gravitational perturbations and quantifies their scale in cosmological and black hole contexts.

Findings

Cosmological horizon fluctuations are typically at the Planck length.

Black hole horizon fluctuations are smaller than Planck length for large black holes.

Black hole fluctuations do not invalidate the semiclassical Hawking process.

Abstract

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.