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A curve whose tangent is parallel transported along itself with respect to a connection.
For pseudo-Riemannian metrics, geodesics need not minimize length; null geodesics have zero proper length.
wp-geodesicnlab-geodesictong-grEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The connection defines geodesics by vanishing covariant acceleration.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-levi_civita_connectionnlab-levi_civita_connectiontong-grwp-geodesicnlab-geodesicEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Free test-body trajectories are represented by timelike or null geodesics under the stated approximation.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-geodesicnlab-geodesictong-grwp-physics-geodesic_motioneinstein-general-relativity