Non-local effective field theory in general relativity (2411.11990v2)

Abstract: Motivated by known facts about effective field theory and non-Abelian gauge theory, we argue that the post-Newtonian approximation might fail even in the limit of weak fields and small velocities under certain conditions. Namely, the post-Newtonian approximation might break down for wide extended bodies with angular momentum, where angular momentum spans significant spacetime curvature. We construct a novel dimensionless quantity that samples this breakdown, and we evaluate it by means of existing analytical solutions of rotating extended bodies and observational data. We give estimates for galaxies and binary systems, as well as our home in the Cosmos, Laniakea. We thus propose that a novel effective field theory of general relativity is needed to account for the onset of nonlocal angular momentum effetcs, with significant consequences for gravitational physics and cosmology at large.

• The paper proposes a new effective field theory that challenges the traditional post-Newtonian approximation in scenarios with significant angular momentum.
• It introduces a dimensionless scalar, α̃, to quantify when standard GR approximations fail in astrophysical systems.
• Results indicate that angular momentum effects may explain discrepancies previously attributed to non-baryonic dark matter in large-scale structures.

Non-local Effective Field Theory in General Relativity

The paper presented by Galoppo and Torrieri explores the limitations of the post-Newtonian approximation within the framework of General Relativity (GR), particularly in scenarios involving wide extended bodies with angular momentum. Their work suggests that, contrary to common assumptions, the post-Newtonian approximation may not always be reliable for weak fields and small velocities under certain conditions. The authors propose the construction of a new dimensionless parameter which they propose as a metric to evaluate the breakdown of the post-Newtonian approximation and, by extension, the need for a novel effective field theory that captures nonlocal general relativistic effects.

The post-Newtonian approximation has historically proven effective across various scales, yet it incorporates non-baryonic dark matter to match observations from the galactic scale onward. This paper proposes that the discrepancies often attributed to dark matter might, in part, be explained by previously unaccounted general relativistic effects, particularly those that emerge in systems with significant angular momentum distributed over varying spacetime curvatures.

A key contribution of this paper is the definition and application of a dimensionless scalar quantity, denoted as $\tilde{\alpha}$, which measures the influence of angular momentum effects over regions of significant curvature variance. The authors argue that a large value of $\tilde{\alpha}$ signals the failure of the post-Newtonian approximation, thereby indicating the necessity for a new effective field theory of GR. They meticulously calculate $\tilde{\alpha}$ for a variety of astrophysical systems, including binary star systems, globular clusters, disc galaxies, and the supercluster Laniakea.

The numerical results reveal that $\tilde{\alpha}$ is significantly small for isolated systems such as binary stars and globular clusters, suggesting that these are well-described by traditional post-Newtonian GR without the need for dark matter. Conversely, $\tilde{\alpha}$ is markedly large for disc galaxies and Laniakea, supporting the hypothesis that angular momentum effects, rather than unknown dark matter, could play a pivotal role. The estimation of $\tilde{\alpha}$ being orders of magnitude above unity in these cases implies a profound inadequacy of conventional post-Newtonian expansions and a potential need for the proposed non-local effective theory of GR.

The exploration of non-Abelian gauge theory analogs further underpins their reasoning, suggesting insights from quantum chromodynamics (QCD) where expansions fail because of the nonlocal interactions intrinsic to non-Abelian fields. This analogy is extended to GR where angular momentum, a nonlocal effect, may lead to significant deviations in astrophysical observations, analogously to quark confinement in QCD.

The implications of this work are multifaceted. Practically, a refined theory could transform our understanding of galactic dynamics and the role of dark matter. Theoretically, it challenges existing paradigms within GR, proposing a new lens through which we can view gravitational interactions at large scales. Looking forward, the authors suggest that a new effective field theory based on $\tilde{\alpha}$ could be developed, akin to methods employed in defining QCD's effective theories centered around Wilson loops and lines.

In conclusion, this paper presents a compelling case for re-evaluating the role and necessity of dark matter within the context of galactic-scale gravitation, urging the scientific community to consider the implications of angular momentum in broadening the scope of general relativity's predictions. The research not only encourages the exploration of nonlocal general relativistic effects but also invites further development of innovative theoretical frameworks that could recalibrate our understanding of gravitational physics in both the astrophysical and cosmological domains.