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We propose a new concept, the transversely trapping surface (TTS), as anextension of the static photon surface characterizing the strong gravity regionof a static/stationary spacetime in terms of photon behavior. The TTS isdefined as a static/stationary timelike surface $S$ whose spatial section is aclosed two-surface, such that arbitrary photons emitted tangentially to $S$from arbitrary points on $S$ propagate on or toward the inside of $S$. We studythe properties of TTSs for static spacetimes and axisymmetric stationaryspacetimes. 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 constantand $M$ is the total mass. The connection between the TTS and the looselytrapped surface proposed by us [arXiv:1701.00564] is also examined.

Extension of photon surfaces and their area: Static and stationary spacetimes