Quantization of gravity through hypersurface foliation

Abstract

We have recently proposed in \cite{Park:2014tia} the quantization of pure 4D Einstein gravity through hypersurface foliation, and observed that the 4D Einstein gravity becomes renormalizable once all (or most) of the unphysical degrees of freedom are removed. In this work, we confirm this observation from a more mathematical angle. In particular, we show that the physical state condition arising from the shift vector constraint connects with the requirement that the manifold admit "totally geodesic (TG) foliation". The TG foliation, in turn, makes it possible to view the 4D manifold as abelian fibration over a 3D base. Associating the abelian fibration with the 4D diffeomorphism leads to reduction of the 4D manifold to 3D, thereby realizing and generalizing the holography of 't Hooft.

15 pages, 1 fig

References in corpus (8)

• 3+1 Formalism and Bases of Numerical Relativity
• Hypersurface foliation approach to renormalization of ADM formulation of gravity
• Lagrangian constraints and renormalization of 4D gravity
• Foliation, jet bundle and quantization of Einstein gravity
• One-loop renormalization of a gravity-scalar system
• Indication for unsmooth horizon induced by quantum gravity interaction
• Reduction of BTZ spacetime to hypersurfaces of foliation
• Revisit of renormalization of Einstein-Maxwell theory at one-loop

Cited by in corpus (9)

• Hypersurface foliation approach to renormalization of ADM formulation of gravity
• Holographic quantization of gravity in a black hole background
• Foliation, jet bundle and quantization of Einstein gravity
• One-loop renormalization of a gravity-scalar system
• Boundary dynamics in gravitational theories
• Foliation-based approach to quantum gravity and applications to astrophysics
• 4D covariance of holographic quantization of Einstein gravity
• Quantum gravitational effects on boundary
• Quantization of gravity and finite temperature effects