Field Quantisations in Schwarzschild Spacetime: Theory versus Low-Energy Experiments

TL;DR

This paper investigates how Hawking particles behave in Schwarzschild spacetime using quantum field theory in curved spacetime, revealing differences from path-integral predictions.

Contribution

It provides a detailed analysis of Hawking particle propagators in Schwarzschild spacetime, highlighting discrepancies with the path-integral approach.

Findings

Hawking particle propagator differs from path-integral formalism predictions.

Quantum field theory in curved spacetime reveals ambiguities in particle concepts.

The study enhances understanding of quantum particles near black hole horizons.

Abstract

Non-relativistic quantum particles in the Earth's gravitational field are successfully described by the Schr\"{o}dinger equation with Newton's gravitational potential. Particularly, quantum mechanics is in agreement with such experiments as free fall and quantum interference induced by gravity. However, quantum mechanics is a low-energy approximation to quantum field theory. The latter is successful by the description of high-energy experiments. Gravity is embedded in quantum field theory through the general-covariance principle. This framework is known in the literature as quantum field theory in curved spacetime, where the concept of a quantum particle is, though, ambiguous. In this article, we study in this framework how a Hawking particle moves in the far-horizon region of Schwarzschild spacetime by computing its propagator. We find this propagator differs from that which follows from the path-integral formalism -- the formalism which adequately describes both free fall and quantum interference induced by gravity.