IAS Physics Group Meeting
Love Symmetry
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Abstract: It has been known for a decade that black holes are the most rigid objects in the universe: their tidal deformations (Love numbers) vanish identically in general relativity in four dimensions. This has represented a naturalness problem in the context of classical worldline effective field theory. In my talk I will present a new symmetry of general relativity (Love symmetry) that resolves this naturalness paradox. I will show that perturbations of rotating (Kerr) black holes enjoy an SL(2,R) symmetry in the suitable defined near zone approximation. This symmetry, while approximate in general, in fact yields exact results about static tidal deformations. This symmetry also implies that generic regular black hole perturbations form infinite-dimensional SL(2,R) representations, and in some special cases these are highest weight representations. It is the structure of these highest weight representations that forces the Love numbers to vanish. All other facts about Love numbers, including their puzzling behavior for higher dimensional black holes, also acquire an elegant explanation in terms of SL(2,R) representation theory.