On a relation between the Bach equation and the equation of geometrodynamics
General Relativity and Quantum Cosmology
2021-10-20 v1
Abstract
The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation plays the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of geometrodynamics.
Keywords
Cite
@article{arxiv.gr-qc/0106025,
title = {On a relation between the Bach equation and the equation of geometrodynamics},
author = {M. V. Gorbatenko and A. V. Pushkin and H. -J. Schmidt},
journal= {arXiv preprint arXiv:gr-qc/0106025},
year = {2021}
}
Comments
16 pages, LaTeX, no figures