Abstract
A metricg ik=η ik+Hξ iξk+2Jξ (iPk) is investigated. WhenJ=0 this reduces to the well-known Kerr metric. Conditions on the vectorp i are obtained under which a geodetic, shear-free null congruenceξ i in the Minkowskian space-time (with metricη ik) will continue to remain geodetic and shear-free in the Riemannian space-time ofg ik. A general solution of Einstein’s equationR ik=σξ iξk is obtained whenp iξi=0 andξ i is twist-free.
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Vaidya, P.C., Bhatt, P.V. A generalized kerr-schild metric. Pramana - J. Phys. 3, 28–34 (1974). https://doi.org/10.1007/BF02847266
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DOI: https://doi.org/10.1007/BF02847266