The observation of a general vector field based on exp* is employed to obtain formulas for the coordinate velocity and coordinate acceleration of a geodesic particle. Our results are shown to reduce to those based on a parallel transport definition of observation in special relativity. In general relativity the difference between the expressions for the coordinate velocity and coordinate acceleration derived from the two definitions of observation is given in terms of the Riemann curvature tensor.

Topics
General relativity, Special relativity, Geodesy, Differential geometry, Vector fields
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Avishai and Ekstein used acceleration covariance together with presymmetry to deduce the equivalence principle of general relativity.
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W. T. Reid, Ordinary Differential Equations (Wiley, New York, 1971).
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© 1982 American Institute of Physics.
1982
American Institute of Physics
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