Contingent relations for Klein–Gordon equations

This paper considers a general set of Einstein–Maxwell fields in 2 + 1-dimensional space. Two broad categories of solutions are discussed, namely solutions of vanishing covariant derivatives (uniform electromagnetic fields) and stationary cyclic symmetric spaces. Subsequently, several major subclasses of solutions arise that may be classified according to the conformal algebra they possess. A key feature of these algebras is the presence of the SO(2)×R Killing group. It is shown that this group and other elements of the conformal algebra of each solution satisfy a special contingency relation with the potential function of the Klein–Gordon equation. (author)