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.

According to general relativity, the gravitational field is coded in a metric of Lorentzian signature on the 4-dimensional spacetimemanifold, 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.

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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