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BRSMG Curinga: cultivar de arroz lançada para as condições de terra firme no Estado do Pará.
bitstream/item/27801/1/Com.Tec.216.pdfVersão eletrônica. 1ª impressão: 2010
Geodesic Lines in Fields of Velocity
This work is a purely syntactic geometric exploration of some few elements,
which are our axioms, that in last instance it is the set of differential
equations whose solutions give the geodesic lines of the Schwarzschild
spacetime. We observe that non new physics principles or postulates will be
introduced in this work. We only link the Bohr's atoms model with the
Einstein's relativity through of a common geometric syntax. To obtain this
common syntax, we will define the {\it extended Lorentz group}, which is
defined to preserve the volume form of the Minkowski spacetime. The
Schwarzschild spacetime will be defined as a manifold associated to a set of
radial fields of velocities within of the four-dimensional Minkowski
vectorially space form. Our procedure includes a comparison of the Newtonian
and the Schwarzschild times along geodesic lines. Our constructions have strong
influence of the Einstein paper about the energy content produced by fields, as
well as by the Schr\"odinger digression about the annihilation of matter. We
define the orbital associated to the Kepler's laws as a set of elliptical
orbits, which have equal eccentricity and equal major semi-axis. Then
identifying the eccentricity with the relativistic velocity we will obtain a
thermodynamic equivalence between the increasing of mass in kinetic form in
special relativity theory and an adiabatic process with degree of freedom equal
to 2. The eccentricity will be the needed velocity to move the revolution
ellipsoid and so to obtain a contraction of its major axis such that it
converts into a sphere with radius given by the minor semi-axis. Therefore we
can associate to the each class of equal eccentricity orbital an unique
timelike unit vector, which is called {\it the observer} of class.Comment: 39 page
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