A metricgik=ηik+Hξiξk+2Jξ(iPk) is investigated. WhenJ=0 this reduces to the well-known Kerr metric. Conditions on the vectorpi are obtained under which a geodetic, shear-free null congruenceξi in the Minkowskian space-time (with metricηik) will continue to remain geodetic and shear-free in the Riemannian space-time ofgik. A general solution of Einstein’s equationRik=σξiξk is obtained whenpiξi=0 andξi is twist-free.
Volume 94, 2020
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