Purely Magnetic Spacetimes

Abstract

Purely magnetic spacetimes, in which the Riemann tensor satisfies $R_{abcd}{u}^b{u}^d=0$ 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.

12 pages, standard latex. Submitted to Classical and Quantum Gravity.

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