# Marginally Outer Trapped Surface (MOTS) ## Numerical methods ### Time symmetric - method introduced in [[BoothHennigarPook-Kolb2021]] - equations reviewed in [[2021#Pook-Kolb, Hennigar, Booth]] - can be done in Mathematica with NDSolve ### Time evolved data - [[2018#Pook-Kolb, Birnholtz, Krishnan, Schnetter]] - needs Einstein toolkit ## Relation to minimal surface - $k_{u}=0 \Longrightarrow 2 \Theta_{+}=-\Theta_{-}$ - both expansions vanish iff $k_N=0$ - reduces to minimal surface - these minimal surfaces cannot touch each other with a common tangent vector - otherwise, by the maximum principle for elliptic operators, they must coincide - see [[MostaAnderssonMetzgerSzilagyiWinicour2015]][](https://arxiv.org/abs/1501.05358) ## Further studies - [[0595 Quasi-local energy|quasi-local mass]]: [[2023#Pook-Kolb, Zhao, Andersson, Krishnan, Yau]] ## Related - [[0285 Brill-Lindquist initial data]]