Contents

Idea

Given a point in Minkowski spacetime, its light cone is the subspace of all lightlike vectors at that point.

More generally for a point $x$ in a Lorentzian manifold $(X,g)$, its lightcone is the lightcone in the tangent space $T_x X$.

Sometimes one also calls the collection of all time-like vectors the light cone, then denoted $V_x \subset T_x X$. On a time oriented spacetime this decomposes into the future cone $V_x^+$ and the past cone $V_x^-$.

All these are conical sets.

Related concepts

• causal cone

• celestial sphere