Seminarium Teorii Względności i Grawitacji

We examine the Newman-Janis algorithm's application to an exact regular static solution sustained by a minimally coupled scalar field with a non-standard kinetic term. Although coordinate complexification leads to a regular Kerr-like black hole, we are facing discrepancies in Einstein's equations in a fairly small domain, for which the regularizing parameter is responsible. We also present some regular cosmological solutions free of singularities, undergoing the crossing of the phantom divide line. Some general questions concerning the search for solutions of the Einstein equations and the singularities treatment are briefly discussed.