lightlike

Lightlike is a term used in physics and differential geometry to describe a property of vectors or separations in spacetime that has zero length under the spacetime metric. It is most closely associated with the paths that light rays follow in vacuum and with massless particles such as photons.

In special relativity and general relativity, a four-vector v is lightlike (also called null) if its Minkowski or spacetime norm vanishes. With the common signature (-,+,+,+), this means η(v,v) = 0, which for a displacement (c dt, dx, dy, dz) reads c^2 dt^2 = dx^2 + dy^2 + dz^2. The set of all lightlike vectors at a point forms the light cone, separating timelike and spacelike directions.

A null or lightlike worldline is a curve whose tangent vector is lightlike everywhere. Photons travel along null geodesics, the straightest possible paths in curved spacetime. Timelike geodesics describe massive particles, which experience proper time along their worldlines, whereas lightlike paths have zero proper time.

Lightlike separations between events imply zero interval and are capable of causal influence only at the speed of light. They define the boundary of the causal structure of spacetime: events connected by a lightlike interval lie on the light cone of each event.

In curved spacetime, the concept remains, with null surfaces and null geodesics playing central roles in phenomena such as black hole horizons and gravitational lensing. Lightlike is sometimes referred to as null, and in some mathematical contexts as isotropic, though the terminology may vary by field.