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

TL;DR

This paper develops a systematic method to couple gravity with Goldstone fields arising from spontaneously broken space-time symmetries, applying it to systems like superfluids, membranes, and spinning objects such as neutron stars.

Contribution

It introduces a general coset construction approach to couple gravity with non-linearly realized space-time symmetries, providing a clear parametrization of degrees of freedom in various physical systems.

Findings

Systematic coupling of gravity with Goldstone fields for broken space-time symmetries.

Application to models of superfluids, membranes, and spinning astrophysical objects.

Unambiguous parametrization of degrees of freedom in these systems.

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.