Hidden symmetry of the static response of black holes: applications to Love numbers

A bstract We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms centrally extended Schrödinger algebra $$ \mathfrak{sh} sh (1) = \mathfrak{sl} sl (2 , ℝ) ⋉ \mathcal{H} H . The central charge is given by the hole mass, echoing results on entropy from near-horizon diffeomorphism symmetry. finite symmetry transformations generated these correspond to Galilean and conformal field coordinates. This new structure allows one discuss response in test approximation symmetry-based approach First we (horizontal) protecting vanishing Love numbers recently exhibited Hui et al., dubbed HJPSS symmetry, coincides with generators group. Then, it demonstrated selected thanks spontaneous breaking full at horizon down simple abelian sub-group. latter can be understood as regularity horizon. In 4-dimensional case, this provides protection for numbers. Our trivially extend Kerr case.