Stationary, charged Zipoy-Voorhees metric from colliding wave spacetime

Abstract

Through the Ernst formalism we provide expression for a class of colliding Einstein-Maxwell (EM) metrics with cross polarization. Local isometry is imposed as a means to transform interaction region of the spacetime into stationary, charged Zipoy-Voorhees (ZV) metric in Schwarzschild coordinates. This is known as the Chandrasekhar-Xanthopoulos (CX) duality which maps the plane of double-null coordinates (with two spacelike cyclic coordinates) to the static/stationary spacetime. The ZV-metric is known to describe planetary/stellar objects with arbitrary distortion parameter. Asymptotic behaviour of the metric for practical use is provided. The world may be seen in a grain of sand - William Blake.