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Geodesics in general relativity

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

For broader coverage of this topic, see Geodesics.

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

Geodesic

Geodetic precession

Schwarzschild geodesics

Geodesics as Hamiltonian flows

Synge's world function

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, (1972) John Wiley & Sons, New York ISBN 0-471-92567-5. See chapter 3.

Steven Weinberg

and Evgenii M. Lifschitz, The Classical Theory of Fields, (1973) Pergammon Press, Oxford ISBN 0-08-018176-7 See section 87.

Lev D. Landau

Kip S. Thorne, John Archibald Wheeler, Gravitation, (1970) W.H. Freeman, New York; ISBN 0-7167-0344-0.

Charles W. Misner

A first course in general relativity, (1985; 2002) Cambridge University Press: Cambridge, UK; ISBN 0-521-27703-5. See chapter 6.

Bernard F. Schutz

General Relativity, (1984) The University of Chicago Press, Chicago. See Section 3.3.

Robert M. Wald