Null hypersurface

In differential geometry, a null hypersurface of a Lorentzian manifold is a manifold of dimension one less than the Lorentzian manifold, such that the tangent space at any point contains vectors that are all space-like except in one direction, in which vectors have a null "length". The metric applied to such a vector and any other vector in the tangent space (including the vector itself) is null. Another way of saying this is that the pullback of the metric onto the tangent space is degenerate.

In space-time, a null hyperspace is a 3-dimensional manifold whose tangent spaces are space-like except that they contain one line corresponding to the world-line of a particle moving at the speed of light. For example, a light cone is a null hypersurface. Another example is a Killing horizon or the event horizon of a black hole.

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