  We study timelike, totally umbilic hypersurfaces -- called photon surfaces --
in $n+1$-dimensional static, asymptotically flat spacetimes, for $n+1\geq4$.
First, we give a complete characterization of photon surfaces in a class of
spherically symmetric spacetimes containing the (exterior) subextremal
Reissner--Nordstr\"om spacetimes, and hence in particular the (exterior)
positive mass Schwarzschild spacetimes. Next, we give new insights into the
spacetime geometry near equipotential photon surfaces and provide a new
characterization of photon spheres (not appealing to any field equations).
  We furthermore show that any asymptotically flat electrostatic electro-vacuum
spacetime with inner boundary consisting of equipotential, (quasi-locally)
subextremal photon surfaces and/or non-degenerate black hole horizons must be
isometric to a suitable piece of the necessarily subextremal
Reissner--Norstr\"om spacetime of the same mass and charge. Our uniqueness
result applies work by Jahns and extends and complements several existing
uniqueness theorems. Its proof fundamentally relies on the lower regularity
rigidity case of the Riemannian Positive Mass Theorem.
