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We present a simple approach for obtaining Kerr interior solutions with thehelp of the Newman-Janis algorithm (NJA) starting with static space-timesdescribing physically sensible interior Schwarzschild solutions. In thiscontext, the Darmois-Israel (DI) junction conditions are analyzed. Startingfrom the incompressible Schwarzschild solution, a class of Kerr interiorsolutions is presented, together with a discussion of the slowly rotatinglimit. The energy conditions are discussed for the solutions so obtained.Finally, the NJA algorithm is applied to the static, anisotropic, conformallyflat solutions found by Stewart leading to interior Kerr solutions with oblatespheroidal boundary surfaces.Comment: 15 pages, version published in IJMP

INTERIOR KERR SOLUTIONS WITH THE NEWMAN–JANIS ALGORITHM STARTING WITH STATIC PHYSICALLY REASONABLE SPACE–TIMES