Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes

Abstract

The near-zone “Love” symmetry resolves the naturalness issue of black hole Love number vanishing with SL (2, ℝ) representation theory. Here, we generalize this proposal to 5-dimensional asymptotically flat and doubly spinning (Myers-Perry) black holes. We consider the scalar response of Myers-Perry black holes and extract its static scalar Love numbers. In agreement with the naturalness arguments, these Love numbers are, in general, non-zero and exhibit logarithmic running unless certain resonant conditions are met; these conditions include new cases with no previously known analogs. We show that there exist two near-zone truncations of the equations of motion that exhibit enhanced SL (2, ℝ) Love symmetries that explain the vanishing of the static scalar Love numbers in the resonant cases. These Love symmetries can be interpreted as local SL (2, ℝ) SL (2, ℝ) near-zone symmetries spontaneously broken down to global SL (2, ℝ) × U (1) symmetries by the periodic identification of the azimuthal angles. We also discover an infinite-dimensional extension of the Love symmetry into SL (2, ℝ) ltimes hat{U}{(1)}_{mathcal{V}}^2 that contains both Love symmetries as particular subalgebras, along with a family of SL (2, ℝ) subalgebras that reduce to the exact near-horizon Myers-Perry black hole isometries in the extremal limit. Finally, we show that the Love symmetries acquire a geometric interpretation as isometries of subtracted (effective) black hole geometries that preserve the internal structure of the black hole and interpret these non-extremal SL (2, ℝ) structures as remnants of the enhanced isometry of the near-horizon extremal geometries.