Gravitational closure of weakly birefringent electrodynamics

TL;DR

This paper derives a new family of gravitational field equations based on the causal structure of weakly birefringent electrodynamics, enabling predictions of vacuum birefringence phenomena.

Contribution

It introduces a gravitational closure method to derive tensorial gravitational dynamics from the most general linear electrodynamics with weak birefringence.

Findings

Eleven-parameter family of weak gravitational field equations

Predicts conditions for vacuum birefringence occurrence

Links electrodynamics properties to gravitational dynamics

Abstract

We derive the gravitational dynamics of the tensorial geometry which underlies the most general linear theory of electrodynamics that features weak birefringence in vacuo. This derivation is performed by way of gravitational closure, which is a mechanism that employs the causal structure of any canonically quantizable matter dynamics on some tensorial spacetime geometry in order to derive canonical dynamics for the latter. The resulting eleven-parameter family of weak gravitational field equations allows to predict where vacuum birefringence will occur, if there is any.