Purely Magnetic Spacetimes

Purely magnetic spacetimes, in which the Riemann tensor satisfies $R_{abcd}u^bu^d=0$ for some unit timelike vector $u^a$, are studied. The algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given to the uniqueness of $u^a$. Some remarks concerning the nature of the congruence associated with $u^a$ are made.