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Title: Conformal geometrodynamics regained: Gravity from duality

There exist several ways of constructing general relativity from ‘first principles’: Einstein’s original derivation, Lovelock’s results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and Hojman–Kuchař-Teitelboim’s derivation of the Hamiltonian form of the theory from the symmetries of space–time, to name a few. Here I propose a different set of first principles to obtain general relativity in the canonical Hamiltonian framework without presupposing space–time in any way. I first require consistent propagation of scalar spatially covariant constraints (in the Dirac picture of constrained systems). I find that up to a certain order in derivatives (four spatial and two temporal), there are large families of such consistently propagated constraints. Then I look for pairs of such constraints that can gauge-fix each other and form a theory with two dynamical degrees of freedom per space point. This demand singles out the ADM Hamiltonian either in (i) CMC gauge, with arbitrary (finite, non-zero) speed of light, and an extra term linear in York time, or (ii) a gauge where the Hubble parameter is conformally harmonic.
Authors:
Publication Date:
OSTI Identifier:
22451154
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DEGREES OF FREEDOM; GENERAL RELATIVITY THEORY; GEOMETRY; GRAVITATION; HAMILTONIANS; SYMMETRY; TENSORS