  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.
