  In asymptotically flat spacetimes, bearing the null geodesics reaching the
future null infinity in mind, we propose new concepts, the "dark horizons" as
generalizations of the photon sphere. They are defined in terms of the
structure of escape/capture cones of photons with respect to a unit timelike
vector field. More specifically, considering a two-sphere that represents a set
of emission directions of photons, the dark horizons are located at positions
where a hemisphere is marginally included in the capture and escape cones,
respectively. We show that both of them are absent in the Minkowski spacetime,
while they exist in spacetimes with black hole(s) under a certain condition. We
derive the general properties of the dark horizons in spherically symmetric
spacetimes and explicitly calculate the locations of the dark horizons in the
Vaidya spacetime and the Kerr spacetime.
