  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 $16 \pi m^2 + 4 \pi a^2$ (compared to the familiar $16 \pi
m^2 - 4 \pi a^2$ 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 $2 \pi (1-\sqrt{1-(a/m)^2})$. 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 $0 \leq a/m \leq 1$ (compared to $0 \leq a/m \leq
\sqrt{3}/2$ for the horizon).
