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

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 |A₀| of a TTS is proved to be bounded as |A₀≤ 4π(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 [Prog. Theor. Exp. Phys. 2017, 033E01 (2017)] is also examined.