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]

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

Geometric transport along circular orbits in stationary axisymmetric spacetimes

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.Comment: 33 pages ijmpd latex article with 24 eps figure

The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor

The scale invariant Petrov classification of the Weyl tensor is linked to the scale invariant combination of the Kasner index constraints, and the Lifshitz-Khalatnikov Kasner index parametrization scheme turns out to be a natural way of adapting to this symmetry, while hiding the permutation symmetry that is instead made manifest by the Misner parametrization scheme. While not so interesting for the Kasner spacetime by itself, it gives a geometrical meaning to the famous Kasner map transitioning between Kasner epochs and Kasner eras, equivalently bouncing between curvature walls, in the BLK-Mixmaster dynamics exhibited by spatially homogeneous cosmologies approaching the initial cosmological singularity and the inhomogeneous generalization of this dynamics.Comment: 16 page Latex cimento.cls formatted document with 6 EPS figures annd 2 PicTeX figures; to appear in the Proceedings of the First Italian-Pakistan Workshop on Relativistic Astrophysics which will be published as a special issue of Nuovo Cimento

Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

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