A first-principles derivation of York scaling and the Lichnerowicz-York equation

Simple item page
dc.creatorAnderson, Edward
dc.creatorBarbour, Julian
dc.creatorFoster, Brendan Z.
dc.creatorKelleher, Bryan
dc.creatorO'Murchadha, Niall
dc.date2004-04-22
dc.date.accessioned2026-07-07T03:28:38Z
dc.date.available2026-07-07T03:28:38Z
dc.descriptionThe only efficient and robust method of generating consistent initial data in general relativity is the conformal technique initiated by Lichnerowicz and perfected by York. In the spatially compact case, the complete scheme consists of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition, and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the Lichnerowicz-York equation for the conformal factor (psi) of the physical metric (psi)^4(g_{ij}) given an initial unphysical 3-metric (g_{ij}). The CMC condition and LFE introduce a distinguished foliation (definition of simultaneity) on spacetime, and separate scaling laws for the canonical momenta and their trace are used. In this article, we derive all these features in a single package by seeking a gauge theory of geometrodynamics (evolving 3-geometries) invariant under both three-dimensional diffeomorphisms and volume-preserving conformal transformations.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/gr-qc/0404099
dc.identifierhttp://arxiv.org/abs/gr-qc/0404099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34904
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA first-principles derivation of York scaling and the Lichnerowicz-York equation
dc.typetext

Files

Collections

arXiv