Geroch group for Einstein spaces and holographic integrability
Abstract
We review how Geroch's reduction method is extended from Ricci-flat to Einstein spacetimes. The Ehlers-Geroch SL(2,R) group is still present in the three-dimensional sigma-model that captures the dynamics, but only a subgroup of it is solution-generating. Holography provides an alternative three-dimensional perspective to integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes. These properties emerge as conditions on the boundary data (metric and energy-momentum tensor) ensuring that the hydrodynamic derivative expansion be resummed into an exact four-dimensional Einstein geometry. The conditions at hand are invariant under a set of transformations dubbed holographic U-duality group. The latter fills the gap left by the Ehlers-Geroch group in Einstein spaces, and allows for solution-generating maps mixing e.g. the mass and the nut charge.
Keywords
Cite
@article{arxiv.1512.04970,
title = {Geroch group for Einstein spaces and holographic integrability},
author = {Anastasios C. Petkou and P. Marios Petropoulos and Konstantinos Siampos},
journal= {arXiv preprint arXiv:1512.04970},
year = {2015}
}
Comments
v1: 1+24 pages, Latex, imbrication with arXiv:1403.6511 in sections 2 and 3. arXiv admin note: text overlap with arXiv:1510.06456