= Non-null hypersurface projection
{title2=$P^a{}_b=\delta^a{}_b-\varepsilon n^an_b,\quad\varepsilon=n_an^a=\pm1$}
A <non-null hypersurface projection> annihilates the unit <normal vector> and fixes tangent vectors to the <hypersurface>. It obeys $P^2=P$. Apply it to every tensor index to remove normal components, with the metric used to lower or raise the index pair for covariant slots. For a timelike unit normal in mostly-plus signature it is the <spatial projection tensor>. A null normal cannot be normalized this way, and a null hypersurface requires additional choices for a corresponding projection.
Back to article page
