Showing papers on "Geodesic deviation published in 1963"
TL;DR: In this article, a discussion of the use of the modern, coordinate-free concept of a vector and of computations which are simplified by introducing a vector instead of its components is presented.
Abstract: Fermi coordinates, where the metric is rectangular and has vanishing first derivatives at each point of a curve, are constructed in a particular way about a geodesic. This determines an expansion of the metric in powers of proper distance normal to the geodesic, of which the second‐order terms are explicitly computed here in terms of the curvature tensor at the corresponding point on the base geodesic. These terms determine the lowest‐order effects of a gravitational field which can be measured locally by a freely falling observer. An example is provided in the Schwarzschild metric. This discussion of Fermi Normal Coordinate provides numerous examples of the use of the modern, coordinate‐free concept of a vector and of computations which are simplified by introducing a vector instead of its components. The ideas of contravariant vector and Lie Bracket, as well as the equation of geodesic deviation, are reviewed before being applied.
330 citations
TL;DR: In this article, it was shown that the existence of a relative tensor, i.e., the tensor at a point x with respect to one at a base point x, is physically essential.
Abstract: It is shown that by a description of the gravitational field within the limits of Einstein's theory only a relative gravitational field, i. e. the gravitational field at a point x with respect to one at a point x′, is physically essential. A reflection of curved space-time into continuum of flat spaces Ex′ depending on coordinates of an arbitrary point x′ is made. The relative gravitational field is described by tensor potentials in terms of the two-metric formalism. The relative gravitational field depends on two points: on a current point x and a base point x′. This allows to localize the gravitational field without violating the equivalence principle. Integral conservation laws for energy momentum and angular momentum are obtained, the energy-momentum tensor being a true relative tensor, i. e. a tensor depending on two points: x and x′. All values connected with a gravitational field are relative what is interpreted as the presence of some general relativity in the gravitational field.
8 citations