Back-reaction of quantum processes and modified gravitational dynamics

Abstract: In this paper, we seek to find a modified theory of gravity that accounts for the back-reaction of QED on curved spacetime. It is already known that vacuum fluctuations induce interactions between gravity and photons. An effective action for electromagnetism, which encodes the details of such quantum process, is utilized to get a set of modified Maxwell's equation and a new Lagrangian for the dynamics of gravity. Imposition of Cauchy predictability on these modified Maxwell's equations lead us to a new effective metric, from which the Lagrangian can be calculated. The new Lagrangian for gravity turns out to be a function of not just the higher order derivatives of the metric tensor but also the polarization of the photon. This immediately results in phenomenon such as gravitational birefringence and existence of black holes with polarization dependent event horizons.