Quantum description of gravitational waves generated by a classical source

TL;DR

This paper explores the quantum characteristics of gravitational waves from classical sources, showing they behave as coherent states with Poisson-distributed graviton emission, and establishes when classical descriptions are valid.

Contribution

It provides a quantum framework for gravitational waves generated by classical sources and identifies the conditions under which classical approximations hold.

Findings

Expectation value of GW operator matches classical retarded solution

Mean and variance of emitted gravitons are equal, indicating Poisson statistics

Classical approximation is valid for astrophysical sources but not always for laboratory systems

Abstract

We investigate the quantum properties of gravitational waves (GWs) generated by a classical energy-momentum tensor. Treating the GW field as a quantum field coupled to a classical source, we evaluate the expectation value of the GW operator. We demonstrate that this expectation value exactly reproduces the classical retarded solution. Furthermore, we show that the mean and variance of the number of emitted gravitons are equal. This suggests that the graviton emission is a Poisson process, as expected for a coherent state. We establish a quantitative criterion for the validity of the classical wave description. By applying this criterion, we find that the classical approximation is remarkably accurate for astrophysical sources, but laboratory-scale systems may reside in a regime where the discrete nature of graviton emission becomes significant.