the vacuum character of a CFT [@Maloney:2007ud]. In the following we will refer to any theory of gravity whose one-loop contribution is of the form (\[ZCFT\]) as dual to Einstein gravity or an “ordinary” CFT as opposed to a logarithmic CFT, but we make no further restrictions. As we will see a CFT with zero central charge gives rise to the same character — simply because the same modes are present in the theory — even though they are null modes.

We note here that massless spin-two quasi-normal modes are often dismissed because they are pure gauge, see e.g. [@Sachs:2008gt]. But as is often the case in gravity the asymptotic behavior of the modes tells us whether it is relevant or not. The Einstein modes are large gauge transformations and as shown by Brown and Henneaux [@Brown:1986nw] they are of crucial importance as generating elements of the asymptotic symmetry group. Thus, being interested in the boundary behavior, it is logical to include those modes and that we obtain precisely the CFT vacuum character by summing over those modes that are responsible for non-trivial diffeomorphisms at the boundary.

However, we try to argue in this work that we can *choose* to 