Properties of the instantaneous ergo surface of a Kerr black hole

This paper explores properties of the instantaneous ergo surface of a Kerr black hole. The surface area is evaluated in closed form. In terms of the mass (m) and angular velocity (a), to second order in a, the area of the ergo surface is given by 16 pim(2) + 4 pia(2) (compared to the familiar 16 pim(2) - 4 pia(2) for the event horizon). Whereas the total curvature of the instantaneous event horizon is 4 pi, on the ergo surface it ranges from 4 pi (for a = 0) to 0 (for a = m)due to conical singularities on the axis (theta = 0, pi) of deficit angle 2 pi (1-root1-(a/m)(2)). A careful application of the Gauss-Bonnet theorem shows that the ergo surface remains topologically spherical. Isometric embeddings of the ergo surface in Euclidean 3-space are defined for 0 less than or equal to a/m less than or equal to 1 (compared to 0 less than or equal to a/m less than or equal to root3/2 for the horizon).