Hidden Symmetry of Vanishing Love

          @misc{ pirsa_PIRSA:21060079,
            doi = {10.48660/21060079},
            url = {https://pirsa.org/21060079},
            author = {Ivanov, Mikhail},
            keywords = {Other},
            language = {en},
            title = {Hidden Symmetry of Vanishing Love},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060079 see, \url{https://pirsa.org}}
          }
          

Abstract

We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden infinite-dimensional ("Love") symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses (Love numbers) of static and spinning black holes. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. The Love symmetry contains an SL(2,R)×U(1) subalgebra. Generic regular solutions of the near zone Teukolsky equation form infinite-dimensional SL(2,R) representations. In some special cases these are highest weight representations. This situation corresponds to vanishing Love numbers. In particular, static perturbations of four-dimensional Schwarzschild black holes belong to finite-dimensional representations. Other known facts about static Love numbers also acquire an elegant explanation in terms of the SL(2,R) representation theory.