  As discussed in the paper, in a matter-filled spacetime, perhaps with
positive cosmological constant, a stable marginally outer trapped 2-sphere must
satisfy a certain area inquality. Namely, its area must be bounded above by
$4\pi/c$, where $c > 0$ is a lower bound on a natural energy momentum term. In
this note we consider the rigidity that results for stable, or weakly
outermost, marginally outer trapped 2-spheres that achieve this upper bound on
the area. The "canonical" dynamical horizon in Vaidya spacetime and certain
spacelike hypersurfaces in Nariai spacetime provide illustrations of the main
results. These results may be viewed as spacetime analogues of the rigidity
results of Bray, Brendle and Neves [10] concerning area minimizing 2-spheres in
Riemannian 3-manifolds with scalar curvature having positive lower bound.
