  The imposition of a constraint between the metric tensor elements in both
three- and four-dimensional, rotating AdS space-times is shown to reduce the
number of independent equations of motion and to result in new families of
solutions to the equations of motion. For the geometries investigated analytic
solutions or partial analytic solutions of the equations of motion are
obtained. In all cases the number of independent field equations is less than
the number of independent functions, resulting in an undetermined function
which can be freely specified. For rotating, asymptotically $AdS$ space-times
the reduction of the number of field equations to be solved holds for vacuum
black hole solutions and for black hole solutions obtained from space-times
containing matter.
