Develop an alpha-based nonlocal effective field theory for general relativity

Develop an explicit effective field theory for general relativity organized as a systematic expansion in the proposed dimensionless nonlocal parameter tilde-alpha, constructed from the Riemann curvature tensor and orbital angular momentum tensors over spatial volume elements, that yields calculable corrections to the post-Newtonian approximation for extended rotating systems where tilde-alpha is non-negligible.

Background

The paper argues that the post-Newtonian approximation can fail even in weak-field, slow-motion regimes when applied to extended bodies with significant angular momentum spanning regions of varying curvature. Motivated by analogies with non-Abelian gauge theories, the authors introduce a dimensionless, nonlocal parameter (tilde-alpha) built from the Riemann curvature and special-relativistic orbital angular momentum tensors integrated over volume elements to track the breakdown of post-Newtonian effective field theory.

They estimate tilde-alpha for binaries, a globular cluster, a disc galaxy, and the Laniakea supercluster, finding it small for systems well-described by post-Newtonian methods and extremely large for galaxies and Laniakea. This motivates the need for a new effective theory applicable when tilde-alpha is large, but the authors explicitly state that such an alpha-based effective theory capable of producing concrete corrections to the post-Newtonian expansion is currently not available.