  In this paper we present a new approach to the study of asymptotically flat
static metrics arising in general relativity. In the case where the static
potential is bounded, we introduce new quantities which are proven to be
monotone along the level set flow of the potential function. We then show how
to use these properties to detect the rotational symmetry of the static
solutions, deriving a number of sharp inequalities. As a consequence of our
analysis, a simple proof of the classical $3$-dimensional Black Hole Uniqueness
Theorem is recovered and some geometric conditions are discussed under which
the same statement holds in higher dimensions.
