Static response and Love numbers of Schwarzschild black holes
  We derive the quadratic action for the physical degrees of freedom of
massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild--(A)dS
background in arbitrary dimensions. We then use these results to compute the
static response of asymptotically flat Schwarzschild black holes to external
fields. Our analysis reproduces known facts about black hole Love numbers, in
particular that they vanish for all types of perturbation in four spacetime
dimensions, but also leads to new results. For instance, we find that neutral
Schwarzschild black holes polarize in the presence of an electromagnetic
background in any number of spacetime dimensions except four. Moreover, we
calculate for the first time black hole Love numbers for vector-type
gravitational perturbations in higher dimensions and find that they generically
do not vanish. Along the way, we shed some light on an apparent discrepancy
between previous results in the literature, and clarify some aspects of the
matching between perturbative calculations of static response on a
Schwarzschild background and the point-particle effective theory
