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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
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
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
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