MINKOWSKI SPACE | HYPERSURFACE

An alternative characterization is that the tangent space of a hypersurface contains a nonzero vector such that the metric applied to such a vector and any vector in the tangent space is zero. Another way of saying this is that the pullback of the metric onto the tangent space is degenerate.

For a Lorentzian metric, all the vectors in such a tangent space are space-like except in one direction, in which they are null. Physically, there is exactly one lightlike worldline contained in a null hypersurface through each point that corresponds to the worldline of a particle moving at the speed of light, and no contained worldlines that are time-like. Example of null hypersurfaces include a light cone, a Killing horizon, and the event horizon of a black hole.

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