Covariant Constructive Gravity

TL;DR

This paper introduces a method to construct covariant gravitational equations for tensorial field theories, ensuring diffeomorphism invariance and causality, by solving a PDE system via a power series approach.

Contribution

It develops a systematic approach to derive perturbative gravitational equations that are covariant and causal for arbitrary tensorial matter fields.

Findings

Derived a PDE system for gravitational Lagrangian

Established conditions for causality in gravitational equations

Provided a power series solution method

Abstract

We present a method of constructing perturbative equations of motion for the geometric background of any given tensorial field theory. Requiring invariance of the gravitational dynamics under spacetime diffeomorphisms leads to a PDE system for the gravitational Lagrangian that can be solved by means of a power series ansatz. Furthermore, in each order we pose conditions on the causality of the gravitational equations, that ensure coevolution of the matter fields and the gravitational background is possible, i.e. gravitational equations and matter equations share the same initial data hypersurfaces.