Separability of string equilibrium equations in a generalised Kerr-de Sitter background

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Abstract
The equilibrium conditions for a cosmic string in a stationary asymptotically flat Kerr black hole background have been shown to be separable. It is shown that the algebraic conditions for the background metric to allow such separability are more restrictive than those required merely for simple geodesic Hamilton-Jacobi separability. However they are not more severe than, but just equivalent to, those required for separation of the scalar wave equation as well, for which the corresponding vacuum solutions of the Einstein-Maxwell equations with the cosmological Lambda term have turned out to satisfy even more restrictive conditions giving higher spin separability. This class of solutions in which the string equilibrium equations are thus automatically separable (in the rest frame of the primary Killing vector) includes members interpretable as representing equilibrium states of a rotating black hole in an asymptotically de Sitter background.