  We analyze the constraint equation giving allowed solutions describing fields
and currents in a force-free magnetosphere around a rotating black hole.
Utilizing the divergence properties of the energy and angular-momentum fluxes
for physically allowed solutions, we conclude that poloidal surfaces are
independent of the radial coordinate for large values of $r$. Using this fact
and the Znajek regularity condition, we explicitly derive all possible exact
solutions admitted by the constraint equation for $r$ independent poloidal
surfaces, which are given in terms of the electromagnetic angular velocity
function $\Omega = 1/a\sin^2\theta$, where $a$ is the angular momentum per unit
mass of the black hole.
