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Résumé |
I will present a symmetry argument for the vanishing and non-renormalization of static Love numbers for
spherically symmetric black holes at nonlinear order, in D=4 classical General Relativity. The symmetry is
realized both in full GR and in the worldline EFT, allowing for a unified treatment. This clarifies the naturalness
of vanishing static Love numbers in the worldline EFT when including non-linearities, and extends previous
vanishing results to all nonlinear static tides. When extended to higher dimensional gravity, this also explains
the pattern of vanishing and running static Love numbers of electric and tensor type, and predicts new results
at the nonlinear order. I will also apply the same arguments to the tidal response of shift-symmetric scalar
fields, predicting new zeros and unifying them with the no-hair theorem for shift-symmetric scalar fields (and
its violations). If time permits, I will also comment on the extension of these results to backgrounds with
electro-magnetic and gravito-magnetic charges. Based on joint work with Julio Parra-Martinez. |
