Purely Magnetic Spacetimes

TL;DR

This paper investigates purely magnetic spacetimes where the Riemann tensor's properties impose specific algebraic conditions on the Weyl and Ricci tensors, exploring their structure, uniqueness, and associated congruences.

Contribution

It provides a detailed algebraic analysis of purely magnetic spacetimes and examines the uniqueness of the defining timelike vector.

Findings

Algebraic constraints on Weyl and Ricci tensors identified

Conditions for the uniqueness of the timelike vector u^a analyzed

Implications for the structure of purely magnetic spacetimes discussed

Abstract

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.