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Encyclopedia > Lightlike

In physics, the adjective light-like refers to a contour in spacetime in the context of special relativity whose proper length vanishes. A synonym of "light-like" (which is chosen because the worldline of a light ray is an example of a light-like curve) is null (because the proper length equal zero).

This word is used for higher-dimensional manifolds (or surfaces), too, in which case it means that at least one direction at each point is null.

  Results from FactBites:
1 Introduction (2155 words)
According to general relativity, the gravitational field is coded in a metric of Lorentzian signature on the 4-dimensional spacetime manifold, and the light rays are the lightlike geodesics of this spacetime metric.
From a mathematical point of view, the theory of gravitational lensing is thus the theory of lightlike geodesics in a 4-dimensional manifold with a Lorentzian metric.
In anisotropic or dispersive media, however, the light rays are not the lightlike geodesics of a Lorentzian metric.
3.1 Criteria for multiple imaging in globally hyperbolic spacetimes (562 words)
For geodesics in Riemannian manifolds (i.e., in the positive definite case), an analogous statement holds if the Riemannian metric is complete and is known as Poincaré theorem [280, 350].
along two “infinitesimally close” lightlike geodesics, the name “cut point” may be considered as justified also in this case.
This question is closely related to the question of whether in a complete Riemannian manifold the conjugate locus of a point is closed.
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