  The purpose of the present article is to show that the Newman-Janis and
Newman et al algorithm used to derive the Kerr and Kerr-Newman metrics
respectively, automatically leads to the extension of the initial non negative
polar radial coordinate r to a cartesian coordinate r' running from -\infty to
+\infty, thus introducing in a natural way the region -\infty < r' < 0 in the
above spacetimes. Using Boyer-Lindquist and ellipsoidal coordinates, we discuss
some geometrical aspects of the positive and negative regions of r', like
horizons, ergosurfaces, and foliation structures.
