On a relation between the Bach equation and the equation of geometrodynamics

Details On a relation between the Bach equation and the equation of geometrodynamics On a relation between the Bach equation and the equation of geometrodynamics

2001-06-07

arxiv.org/abs/gr-qc/0106025v1

Gen.Rel.Grav. 34 (2002) 9-22

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, LaTeX, no figures

Scientific paper

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.

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