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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. |
