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Motivated by the increasing interest in finding physically viable rotatingsources, we present a new class of anisotropic rotating solutions. Theenergy-momentum tensor compatible with the metric is composed of anisotropicmatter with a non-vanishing energy flow around the symmetry axis and vanishingviscosity. The new class of solutions can be used to find new possible sourcesfor the Kerr metric, to obtain new regular black hole solutions and to studygalaxies with a central rotating black hole and an halo of dark matter. As anexample, we obtain a 5-parameter class of solutions representing a two-waytraversable wormhole smoothly matched to the Kerr one and satisfying all energyconditions outside the wormhole for a wide range of parameters, in particularfor compact objects. Finally, with a simple modification of the aforementionedsolution, we obtain a source for Kerr metric with a throat geometry,non-representing a two-way traversable wormhole and satisfying all energyconditions.

A new class of anisotropic rotating fluids and some throat-like sources for Kerr metric as examples