Duality in linearized gravity and holography

Abstract

We consider spherical gravitational perturbations of AdS4 spacetime satisfying general boundary conditions at spatial infinity. Using the holographic renormalization method, we compute the energy–momentum tensor and show that it can always be cast in the form of a Cotton tensor for a dual boundary metric. In particular, axial and polar perturbations obeying the same boundary conditions for the effective Schrödinger wavefunctions exhibit an energy–momentum/Cotton tensor duality at conformal infinity. We demonstrate explicitly that this is holographic manifestation of the electric/magnetic duality of linearized gravity in the bulk, which simply exchanges axial with polar perturbations of AdS4 spacetime. We note that this particular realization of gravitational duality is also valid for perturbations near flat and dS4 spacetime, depending on the value of a cosmological constant.