On Poisson geometries related to noncommutative emergent gravity

Abstract

We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R^D, whose effective metric depends on the embedding as well as on the Poisson structure. We study solutions of the equations of motion for the Poisson structure, focusing on a natural class of solutions such that the effective metric coincides with the embedding metric. This leads to i-(anti-) self-dual complexified Poisson structures in four space-time dimensions with Lorentzian signature. Solutions on manifolds with conformally flat metric are obtained and tools are developed which allow to systematically re-derive previous results, e.g. for the Schwarzschild metric. It turns out that the effective gauge coupling is related to the symplectic volume density, and may vary significantly over space-time. To avoid this problem, we consider in a second part space-time manifolds with compactified extra dimensions and split noncommutativity, where solutions with constant gauge coupling are obtained for several physically relevant geometries.

UWThPh-2011-41. V3: minor improvements, published version

References in corpus (10)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• On the Conformal forms of the Robertson-Walker metric
• Cosmological solutions of emergent noncommutative gravity
• Split noncommutativity and compactified brane solutions in matrix models
• Schwarzschild Geometry Emerging from Matrix Models
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Curvature and Gravity Actions for Matrix Models
• On the geometry of Kähler-Poisson structures
• Static forms of the Robertson-Walker spacetimes

Cited by in corpus (4)

• A note on graviton exchange in emergent gravity scenario
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes
• Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection