The densitized lapse ("Taub function") and the Taub time gauge in cosmology

The role of the Taub time gauge in cosmology is linked to the use of the densitized lapse function instead of the lapse function in the variational principle approach to the Einstein equations. The spatial metric variational equations then become the Ricci evolution equations, which are then supplemented by the Einstein constraints which result from the variation with respect to the densitized lapse and the usual shift vector field. In those spatially homogeneous cases where the least disconnect occurs between the general theory and the restricted symmetry scenario, the recent adjustment of the conformal approach to solving the initial value problem resulting from densitized lapse considerations is seen to be inherent in the use of symmetry-adapted metric variables. The minimal distortion shift vector field is a natural vector potential for the new York thin sandwich initial data approach to the constraints, which in this case corresponds to the diagonal spatial metric gauge. For generic spacetimes, the new approach suggests defining a new minimal distortion shift gauge which agrees with the old gauge in the Taub time gauge, but which also makes its defining differential equation agree with the vector potential equation for solving the supermomentum constraint in any time gauge.Comment: 22 pages, Latex article style, no figure

Stationary spacetimes and the Simon tensor

For stationary vacuum spacetimes the Bianchi identities of the second kind equate the Simon tensor to the Simon-Mars tensor, the latter having a clear geometrical interpretation. The equivalence of these two tensors is broken in the nonvacuum case by additional source energy-momentum terms, but absorbing these source terms into a redefinition of the Simon tensor restores the equality. Explicit examples are discussed for electrovacuum and rigidly rotating matter fields.Comment: To appear on the Proceedings of the International Conference in Honor of Y. Choquet-Bruhat, "Analysis, Manifolds, and Geometric Structures in Physics" Hotel Cala di Mola Porto Azzurro - Isola d'Elba June 24th-26th, 200

A List of References on Spacetime Splitting and Gravitoelectromagnetism

Revised version to be published in the Proceedings of the Encuentros Relativistas Espa\~noles, September, 2000 [ http://hades.eis.uva.es/EREs2000 ]Comment: 22 pages, LaTeX article style. Please send corrections and additions to mailto:[email protected]

The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some familiar stationary axisymmetric spacetimes

The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give a more intuitive picture of their rotational features including spin precession effects, and puts related work of Abramowicz, de Felice, and others on circular orbits in black hole spacetimes into a more general context.Comment: 59 pages latex 2.09, uses ijmpd.sty macros, pictex, epsf.sty for 10 eps figures; typographical corrections made compared to published versio

The Cotton, Simon-Mars and Cotton-York Tensors in Stationary Spacetimes

The Cotton-York and Simon-Mars tensors in stationary vacuum spacetimes are studied in the language of the congruence approach pioneered by Hawking and Ellis. Their relationships with the Papapetrou field defined by the stationary Killing congruence and with a recent characterization of the Kerr spacetime in terms of the alignment between of the principal null directions of the Weyl tensor with those of the Papapetrou field are also investigated in this more transparent language.Comment: 14 pages latex(2e) iopart style, no figure