Year: 2013
Type: article
Abstract: We show that there are two equivalent first order descriptions of $2+1$ gravity with a nonzero cosmological constant. One is the well-known spacetime description, and the other is in terms of evolving conformal geometry. The key tool that links these pictures is Cartan geometry, a generalization of Riemannian geometry that allows for geometries locally modeled off arbitrary homogeneous spaces. The two different interpretations suggest two distinct phase space reductions. The spacetime picture leads to the $2+1$ formulation of general relativity due to Arnowitt, Deser, and Misner, while the conformal picture leads to shape dynamics. Cartan geometry thus provides an alternative to symmetry trading for explaining the equivalence of general relativity and shape dynamics.
Authors: Sean Gryb, Flavio Mercati
Institutions: Utrecht University, University of Nottingham, Perimeter Institute
Language: Latvian
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1967679381