  We propose a new concept, the transversely trapping surface (TTS), as an
extension of the static photon surface characterizing the strong gravity region
of a static/stationary spacetime in terms of photon behavior. The TTS is
defined as a static/stationary timelike surface $S$ whose spatial section is a
closed two-surface, such that arbitrary photons emitted tangentially to $S$
from arbitrary points on $S$ propagate on or toward the inside of $S$. We study
the properties of TTSs for static spacetimes and axisymmetric stationary
spacetimes. In particular, the area $A_0$ of a TTS is proved to be bounded as
$A_0\le 4\pi(3GM)^2$ under certain conditions, where $G$ is the Newton constant
and $M$ is the total mass. The connection between the TTS and the loosely
trapped surface proposed by us [arXiv:1701.00564] is also examined.
