The four-acceleration of a particle executing geodesic motion is zero.
2.
The geodesic motion in curved spacetime, and other things, all depend on the metric.
3.
Einstein s geodesic motion, whereby objects move in a way dictated by the curvature of spacetime.
4.
This contrasts the geodesic motions which are central to the study of Hamilton's principle of least action.
5.
The concept of geodesics becomes central in general relativity, since geodesic motion may be thought of as " pure motion " ( inertial motion ) in spacetime, that is, free from any external influences.
6.
What is so important about the RKHS norm defining the kinetic energy in the action principle is that the vector fields of the geodesic motions of the submanifolds are superpositions of Green's Kernel's.
7.
This approach can be extended to fields rather than a system of particles ( see below ), and underlies the path integral formulation of quantum mechanics, and is used for calculating geodesic motion in general relativity.
8.
A paper published in 1938 by Albert Einstein, Leopold Infeld and Banesh Hoffman showed that if elementary particles are treated as singularities in spacetime, it is unnecessary to postulate geodesic motion as part of general relativity.
9.
This new class of preferred motions, too, defines a geometry of space and time in mathematical terms, it is the geodesic motion associated with a specific covariant concepts, i . e . a description which is valid in any desired coordinate system.
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