The semiclassical approximation to quantum gravity

TL;DR

This paper reviews the semiclassical approximation in quantum gravity, focusing on deriving the functional Schrödinger equation, quantum corrections, and their implications for phenomena like black hole evaporation and decoherence.

Contribution

It provides a comprehensive analysis of the semiclassical approach, including derivations of correction terms and their applications to cosmological and black hole scenarios.

Findings

Quantum gravitational correction terms affect energy levels in De Sitter space.

Non-unitary effects are observed in black hole evaporation models.

Decoherence plays a significant role in semiclassical gravity.

Abstract

A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well as the derivation of quantum gravitational correction terms to the Schr\"odinger equation. These terms are used to calculate energy shifts for fields in De~Sitter space and non-unitary contributions in black hole evaporation. Emphasis is also put on the relevance of decoherence and correlations in semiclassical gravity. The back reaction of non-gravitational quantum fields onto the semiclassical background and the emergence of a Berry connection on superspace is also discussed in this framework.