  We introduce an effective action smoothly extending the standard
Einstein-Hilbert action to include un-gravity effects. The improved field
equations are solved for the un-graviton corrected Schwarzschild geometry
reproducing the Mureika result. This is an important test to confirm the
original ``guess'' of the form of the Un-Schwarzschild metric. Instead of
working in the weak field approximation and ``dressing'' the Newtonian
potential with un-gravitons, we solve the ``effective Einstein equations''
including all order un-gravity effects. An unexpected ``bonus'' of accounting
un-gravity effects is the fractalisation of the event horizon. In the
un-gravity dominated regime the event horizon thermodynamically behaves as
fractal surface of dimensionality twice the scale dimension d_U.
