167 research outputs found
Conformal derivative and conformal transports over spaces with contravariant and covariant affine connections and metrics
Transports preserving the angle between two contravariant vector fields but
changing their lengths proportional to their own lengths are introduced as
''conformal'' transports and investigated over spaces with contravariant and
covariant affine connections (whose components differ not only by sign) and
metrics. They are more general than the Fermi-Walker transports. In an
analogous way as in the case of Fermi-Walker transports a conformal covariant
differential operator and its conformal derivative are defined and considered
over the above mentioned spaces. Different special types of conformal
transports are determined inducing also Fermi-Walker transports for orthogonal
vector fields as special cases. Conditions under which the length of a non-null
contravariant vector field could swing as a homogeneous harmonic oscillator are
established. The results obtained regardless of any concrete field
(gravitational) theory could have direct applications in such types of
theories.
PACS numbers: 04.90.+e; 04.50.+h; 12.10.Gq; 02.40.VhComment: 17 pages, LaTe
Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics
The auto-parallel equation over spaces with affine connections and metrics is
considered as a result of the application of the method of Lagrangians with
covariant derivatives (MLCD) on a given Lagrangian density.Comment: 19 pages, LaTe
Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces
Conditions for the existence of flows with non-null shear-free and
expansion-free velocities in spaces with affine connections and metrics are
found. On their basis, generalized Weyl's spaces with shear-free and
expansion-free conformal Killing vectors as velocity's vectors of spinless test
particles moving in a Weyl's space are considered. The necessary and sufficient
conditions are found under which a free spinless test particle could move in
spaces with affine connections and metrics on a curve described by means of an
auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by
the use of a dilaton field, the dilaton field appears as a scaling factor for
the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv,
04.50.+h, 04.90.+eComment: 20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv
admin note: substantial text overlap with arXiv:gr-qc/001104
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