  We study the deformation caused by the influence of extrinsic curvature on a
vacuum spherically symmetric metric embedded in a five-dimensional bulk. In
this sense, we investigate the produced black-holes and derive general
characteristics such as their masses, horizons, singularities and thermal
properties. As a test, we also study the bending of light near such black-holes
analyzing the movement of a test particle and the modification caused by
extrinsic curvature on its movement. Accordingly, using the asymptotically
conformal flat condition for the extrinsic curvature, an analytical expansion
of a set of \emph{n}-scalar fields can be defined and we show that the
corresponding black holes must be large and constrained in the range of allowed
values $-1/2 \leq n \leq 1.8$. As a result, they are locally thermodynamically
stable, but not globally preferred.
