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Space-time symmetries are a crucial ingredient of any theoretical model inphysics. Unlike internal symmetries, which may or may not be gauged and/orspontaneously broken, space-time symmetries do not admit any ambiguity: theyare gauged by gravity, and any conceivable physical system (other than thevacuum) 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-linearlyrealize spontaneously broken space-time symmetries. This can be done incomplete generality by weakly gauging the Poincare symmetry group in thecontext of the coset construction. To illustrate the power of this method, weconsider three kinds of physical systems coupled to gravity: superfluids,relativistic membranes embedded in a higher dimensional space, and rotatingpoint-like objects. This last system is of particular importance as it can beused to model spinning astrophysical objects like neutron stars and blackholes. Our approach provides a systematic and unambiguous parametrization ofthe degrees of freedom of these systems.

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