Physics
Scientific paper
Sep 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977anihp..27..115b&link_type=abstract
Institut Henri Poincare, Annales, Section A - Physique Theorique, vol. 27, Aug. 16-Sept. 30, 1977, p. 115-144.
Physics
13
Field Theory (Physics), Geodesic Lines, Kinematics, Particle Motion, Relativity, Vector Analysis, Deviation, Electromagnetic Radiation, Frequency Shift, Geodesy, Parameterization, Riemann Manifold, Space-Time Functions, Taylor Series
Scientific paper
The paper starts with a detailed mathematical study of the concept of geodesic deviation in pseudo-riemannian geometry. A generalization of this concept to geodesic deviations of a higher order is then introduced and the second geodesic deviation is investigated in some detail. A geometric interpretation of the set of generalized geodesic deviations is given and applied in general relativity to determine a covariant and local description (with a desired order of accuracy) of test motions which take place in a certain finite neighbourhood of a given world line of an observer. There is also discussed the proper time evolution of two other objects related to geodesic deviation: the space separation vector and the telescopic vector. This last name is given here to a field of null vectors along observer's world line which always point towards the same adjacent world line. The telescopic equations allow to determine the evolution of the frequency shift of electromagnetic radiation sent from and received on neighbouring world lines. On the basis of these equations also certain relations have been derived which connect the frequencies or frequency shifts with the curvature of space-time.
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