An introduction to gravitational waves through electrodynamics: a quadrupole comparison

TL;DR

This paper pedagogically compares gravitational wave emission with electromagnetic quadrupole radiation, clarifying gauge subtleties and analyzing system stability to derive bounds on Newton's constant.

Contribution

It provides a detailed analogy between gravitational and electromagnetic quadrupole radiation, highlighting subtleties and deriving bounds on fundamental constants.

Findings

Power emitted by quadrupoles in both theories compared

Discrepancies in emission explained by gauge choices

Bound system stability analyzed to constrain Newton's constant

Abstract

We present a pedagogical introduction to some key computations in gravitational waves via a side-by-side comparison with the quadrupole contribution of electromagnetic radiation. Subtleties involving gauge choices and projections over transverse modes in the tensorial theory are made clearer by direct analogy with the vectorial counterpart. The power emitted by the quadrupole moment in both theories is computed, and the similarities as well as the origins of eventual discrepancies are discussed. Finally, we analyze the stability of bound systems under radiation emission, and discuss how the strength of the interactions can be established this way. We use the results to impose an anthropic bound on Newton's constant of order $G\lesssim 3\times 10^4\, G_\text{obs}$, which is on par with similar constraints from stellar formation.