Modeling Compact Objects with Effective Field Theory I: The Effective Action

This is part 1 of 3 from the master's thesis: Modeling Compact Objects with Effective Field Theory, supervised by Amanda Weltman. Using the Effective Field Theory framework for extended objects and the coset construction, we build the leading order effective action for the most general compact object allowed in an effective theory of gravity as general relativity. By recognizing the symmetry breaking pattern of a charged spinning compact object, we derive all the covariant building blocks and constraints to build up the relevant invariant operators in the action to all orders. We derive the effective action for a spinning extended object and make the connection to currently used theories, which use conjugates variables. Moreover, we build the action of a charged particle as well, and include the size structure effects, such as tidal deformation, polarization and dissipation in the quasi-static limit. The invariant operators in the action are accompanied by coefficients that encapsulates the properties of the compact object. We match the known coefficients of the effective action from the literature, and point out the unknown ones that are to be derived.