geodesic tensor
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Geodesic deviation equation — In differential geometry, the geodesic deviation equation is an equation involving the Riemann curvature tensor, which measures the change in separation of neighbouring geodesics. In the language of mechanics it measures the rate of relative… … Wikipedia
Geodesic — [ great circle arcs.] In mathematics, a geodesic IPA|/ˌdʒiəˈdɛsɪk, ˈdisɪk/ [jee uh des ik, dee sik] is a generalization of the notion of a straight line to curved spaces . In presence of a metric, geodesics are defined to be (locally) the… … Wikipedia
Geodesic (general relativity) — This article is about the use of geodesics in general relativity. For the general concept in geometry, see geodesic. General relativity Introduction Mathematical formulation Resources … Wikipedia
Torsion tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… … Wikipedia
Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia
Riemann tensor (general relativity) — The Riemann tensor (general relativity) is a mathematical object that describes gravitation and its effects in Einstein s theory of general relativity. Curvature and geodesic deviationThe Riemann tensor can be used to express the idea of… … Wikipedia
Weyl tensor — In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal… … Wikipedia
Scalar-tensor theory — Scalar tensor theories are theories that include a scalar field as well as a tensor field to represent an interaction, especially the gravitational one. Tensor fields and field theory Modern physics tries to derive all physical theories from as… … Wikipedia
Theoretical motivation for general relativity — A Theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special relativity by examining the dynamics of particles in circular orbits about the earth … Wikipedia
Congruence (general relativity) — In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four dimensional Lorentzian manifold which is interpreted physically as a model of spacetime.… … Wikipedia
Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources … Wikipedia
