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 m ass (m) and angular velocity (a), to second order in a, the area of the erg o 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 i nstantaneous 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 (thet a = 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 topological ly 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 (compa red to 0 less than or equal to a/m less than or equal to root3/2 for the ho rizon).