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 in- variant 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.
Date Issued
2016
Publication Type
Conference Item
Subject(s)
Language(s)
en
Author(s)
Petkou, Anastasios C. | |
Petropoulos, P. Marios |
Journal
PoS - proceedings of science
Publisher
Scuola Internazionale Superiore di Studi Avanzati SISSA
ISSN
1824-8039
Access(Rights)
open.access