(Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects

TL;DR

This work develops a unified coset-based framework to couple gravity to Goldstone modes from spontaneous breaking of spacetime symmetries, by weakly gauging the Poincaré group and applying inverse Higgs constraints. By deriving General Relativity from a coset construction and applying the method to relativistic superfluids, membranes, and spinning point-like objects, the authors obtain systematic, coordinate-free actions that reproduce known low-energy theories and reveal geometric interpretations in terms of induced metrics, extrinsic curvature, and covariant derivatives on worldvolumes. The resulting effective actions organize degrees of freedom and corrections via a derivative expansion, providing clear parametrizations of spin and finite-size effects such as moments of inertia and rotational deformations, while offering a scalable route to NRGR-like analyses. Overall, the paper presents a coherent algebraic route to gravity-compatible descriptions of extended and spinning bodies, with potential extensions to dissipation and higher-order finite-size couplings.

Abstract

Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by gravity, and any conceivable physical system (other than the vacuum) is bound to break at least some of them. Motivated by this observation, we study how to couple gravity with the Goldstone fields that non-linearly realize spontaneously broken space-time symmetries. This can be done in complete generality by weakly gauging the Poincare symmetry group in the context of the coset construction. To illustrate the power of this method, we consider three kinds of physical systems coupled to gravity: superfluids, relativistic membranes embedded in a higher dimensional space, and rotating point-like objects. This last system is of particular importance as it can be used to model spinning astrophysical objects like neutron stars and black holes. Our approach provides a systematic and unambiguous parametrization of the degrees of freedom of these systems.