  Let $\mathfrak{k}$ be a nontrivial finite-dimensional Lie algebra of vector
fields on a manifold M, and consider the family of Lorentzian metrics on M
whose Killing algebra contains $\mathfrak{k}$. We show that scalar relative
differential invariants, with respect to a Lie algebra of vector fields on M
preserving $\mathfrak{k}$, can be used to detect the horizons of several
well-known black holes. In particular, using the Lie algebra structure of
$\mathfrak{k}$, we construct a general relative differential invariant of order
0 that always vanishes on $\mathfrak{k}$-invariant Killing horizons.
