Aspects of thermal one-point functions and response functions in AdS black holes

We revisit the problem of analytically computing one-point functions for scalar fields in planar AdS black holes arbitrary dimension, which are sourced by Weyl squared tensor. analyze terms power series expansions around boundary using method Frobenius. clarify pole structure final answer operator mixing, as argued previously Grinberg and Maldacena. generalize techniques to also obtain analytic results slowly modulated spatially varying sources first nontrivial order wave vector dimension. study first-order corrections function global hole at large mass, where we perturb that correspond curvature horizon.