MG15 - Talk detail

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Abstract

We present a method of constructing equations of motion for the geometric background of any given tensorial field theory, order by order, and in a fully covariant way. Requiring invariance of the gravitational dynamics under spacetime diffeomorphisms leads to identities for the gravitational Lagrangian and the corresponding Euler-Lagrange equations. Expanding the Lagrangian in powers of the gravitational field and its derivatives enables us to solve these identities for the expansion coefficients up to the desired order. Furthermore, in each order we pose conditions on the causality of the gravitational equations and thereby on the gravitational equations themselves, which ensure the matter fields and the gravitational background evolve together in consistent causal fashion. As an application of this approach we explicitly construct the first two orders of the equations of motion for an area metric tensor field that presents the geometry underneath birefringent electrodynamics.

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