  We use the extension of the Minimal Geometric Deformation approach, recently
developed to investigate the exterior of a self-gravitating system in the
Braneworld, to identified a master solution for the deformation undergone by
the radial metric component when time deformations are produced by bulk
gravitons. A specific form for the temporal deformation is used to generate a
new exterior solution with a tidal charge $Q$. The main feature of this
solution is the presence of higher-order terms in the tidal charge, thus
generalizing the well known tidally charged solution. The horizon of the black
hole lies inside the Schwarzschild radius, $h<r_s=2\,{\cal M}$, indicating that
extra-dimensional effects weaken the gravitational field.
