  A classical question in general relativity is about the classification of
regular static black hole solutions of the static Einstein-Maxwell equations
(or electrovacuum system). In this paper, we prove some classification results
for an electrovacuum system such that the electric potential is a smooth
function of the lapse function. In particular, we show that an n-dimensional
locally conformally flat extremal electrovacuum space must be in the
Majumdar-Papapetrou class. Also, we prove that any three or four dimensional
extremal electrovacuum space must be locally conformally flat. Moreover, we
prove that an n-dimensional subextremal electrovacuum space with fourth-order
divergence free Weyl tensor and zero radial Weyl curvature such that the
electric potential is in the Reissner-Nordstr\"om class is locally a warped
product manifold with (n-1)-dimensional Einstein fibers. Finally, a three
dimensional subextremal electrovacuum space with third-order divergence free
Cotton tensor was also classified.
