nLab
light cone

Contents

Context

Riemannian geometry

Gravity

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 xx in a Lorentzian manifold (X,g)(X,g), its lightcone is the lightcone in the tangent space T xXT_x X.

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

All these are conical sets.

Last revised on October 31, 2017 at 09:26:03. See the history of this page for a list of all contributions to it.