  We obtain an Einstein metric of constant negative curvature given an
arbitrary boundary metric in three dimensions, and a conformally flat one given
an arbitrary conformally flat boundary metric in other dimensions. In order to
compute the on-shell value of the gravitational action for these solutions, we
propose to integrate the radial coordinate from the boundary till a critical
value where the bulk volume element vanishes. The result, which is a functional
of the boundary metric, provides a sector of the quantum effective action
common to all conformal field theories that have a gravitational description.
We verify that the so-defined boundary effective action is conformally
invariant in odd (boundary) dimensions and has the correct conformal anomaly in
even (boundary) dimensions. In three dimensions and for arbitrary static
boundary metric the bulk metric takes a rather simple form. We explicitly carry
out the computation of the corresponding effective action and find that it
equals the non-local Polyakov action.
