Duality in linearized gravity and holography

TL;DR

This paper explores the duality between energy-momentum and Cotton tensors in linearized gravity on AdS4, revealing a holographic electric/magnetic duality that exchanges axial and polar perturbations and extends to flat and dS4 spaces.

Contribution

It demonstrates a holographic duality between energy-momentum and Cotton tensors in linearized AdS4 gravity, linking boundary conditions to bulk gravitational duality.

Findings

Energy-momentum tensor can be expressed as Cotton tensor at the boundary.

Axial and polar perturbations exhibit a duality exchanging their roles.

The duality extends to flat and dS4 space-times depending on the cosmological constant.

Abstract

We consider spherical gravitational perturbations of AdS4 space-time 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 Cotton tensor for a dual boundary metric. In particular, axial and polar perturbations obeying the same boundary conditions for the effective Schrodinger wave-functions 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 space-time. We note on the side that this particular realization of gravitational duality is also valid for perturbations near flat and dS4 space-time, depending on the value of cosmological constant.