Optical space of the Kerr solutions

In this paper, we discuss the optical geometry of the Kerr solutions, and s how the embedding diagram at the equator theta = pi /2 for the optical spac e of the Kerr solution with a/M = 1. It is noticed that at the equator thet a = pi /2, the Gaussian curvature K for the ordinary space is negative, and the for (k) over tilde the optical space is positive.