2+1 gravity on the conformal sphere

Abstract

We show that there are 2 equivalent first order descriptions of 2+1 gravity with non-zero 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 modelled 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.

29 preprint pages, 3 figures

References in corpus (13)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Quantum Gravity at a Lifshitz Point
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Einstein gravity as a 3D conformally invariant theory
• MacDowell-Mansouri gravity and Cartan geometry
• The Link between General Relativity and Shape Dynamics
• The physical gravitational degrees of freedom
• Tractors, Mass and Weyl Invariance
• Weyl Invariance and the Origins of Mass
• Massive Higher Spins from BRST and Tractors
• Dynamics of Pure Shape, Relativity and the Problem of Time
• Gravity, Cartan geometry, and idealized waywisers
• On a partially reduced phase space quantisation of general relativity conformally coupled to a scalar field

Cited by in corpus (13)

• A Shape Dynamics Tutorial
• Bouncing Unitary Cosmology I: Mini-Superspace General Solution
• The Effective Action of Superrotation Modes
• Schrodinger Evolution for the Universe: Reparametrization
• Poincaré invariance and asymptotic flatness in Shape Dynamics
• Kendall's Shape Statistics as a Classical Realization of Barbour-type Timeless Records Theory approach to Quantum Gravity
• A first-order approach to conformal gravity
• Time and dark matter from the conformal symmetries of Euclidean space
• Holographic Special Relativity
• Linking shape dynamics and loop quantum gravity
• Observing Shape in Spacetime
• Right about time?
• Is Spacetime Countable?