Gravito-magnetic polarization of Schwarzschild black hole

We determine the gravito-magnetic Love numbers of non-rotating black holes in all spacetime dimensions through a novel and direct derivation. The Ishibashi-Kodama master field and its associated field equation are avoided. The matching to the EFT variables is simple. This method allows us to correct the values in the literature. Moreover, we highlight a parity-based selection rule for nonlinear terms that include both electric-type and magnetic-type gravitational field tensors, enabling us to conclude that many of the nonlinear response coefficients in the Schwarzschild black hole effective action vanish.