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

## TL;DR

This paper introduces transversely trapping surfaces (TTS) as an extension of photon surfaces in static and stationary spacetimes, analyzing their properties and establishing an area bound related to the mass of the spacetime.

## Contribution

It defines TTSs as a new concept extending photon surfaces, studies their properties in static and stationary spacetimes, and proves an area bound related to mass.

## Key findings

- TTSs are characterized by photon behavior on or toward their interior.
- The area of TTSs is bounded by $4\pi(3GM)^2$ under certain conditions.
- The connection between TTSs and loosely trapped surfaces is examined.

## Abstract

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.