Comments about "Geodesics in general relativity" in Wikipedia
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Introduction
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Importantly, the world line of a particle free from all external, nongravitational forces is a particular type of geodesic.

That is one of the most simple examples?



In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance).

My understanding is that matter can be described by a stressenergy tensor which physical means that the path of an object follows a geodesic in spacetime.

Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved fourdimensional (4D) spacetime geometry around the star onto threedimensional (3D) space.

My understanding is that I would change space into: space and time.




1. Mathematical expression





The quantity on the lefthandside of this equation is the acceleration of a particle, so this equation is analogous to Newton's laws of motion, which likewise provide formulae for the acceleration of a particle.

My understanding is that a particle can also be a planet or a star considered as a point mass.




2. Equivalent mathematical expression using coordinate time as parameter










3. Derivation directly from the equivalence principle










4. Deriving the geodesic equation via an action










5. Equation of motion may follow from the field equations for empty space










6. Extension to the case of a charged particle










7. Geodesics as curves of stationary interval










8. Derivation using autoparallel transport










9. See also
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Created: 2 March 2019
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