Duality in linearized gravity and holography
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.
Cite
@article{arxiv.0812.0152,
title = {Duality in linearized gravity and holography},
author = {Ioannis Bakas},
journal= {arXiv preprint arXiv:0812.0152},
year = {2009}
}
Comments
22 pages; a few clarifying remarks added at the end of section 6; missing factor sin^2 \theta inserted in eqs. (6.15) and (6.20) (version to be published in Class. Quant. Grav.)