A marginally outer trapped surface in an initial data set 
is a compact two-sided hypersurface whose outward future null
expansion vanishes. With a unit normal 
toward the chosen exterior and the future-normal convention
for 
,
this means
 |
The abbreviation is MOTS. The weaker condition 
defines a weakly future outer trapped surface.
Outermostness, absence of another enclosing weakly trapped surface, and outer area
minimization, a lower area bound for every enclosing surface, are separate hypotheses.
For time-symmetric data 
, a marginally outer trapped surface is a minimal hypersurface.
The equality assertions for the Penrose inequality
specify both outward trapping and the class of enclosing surfaces.
