  We look at the strong field behavior of the Wang-Yau quasi-local energy. In
particular, we examine the limit of the Wang-Yau quasi-local energy as the
defining spacelike 2-surface {\Sigma} approaches an apparent horizon from
outside. Assuming any smooth isometric embedding, we find that the Wang-Yau
quasi-local energy blows up in this limit, unless the horizon can be
isometrically embedded into R3. Moreover, if the horizon cannot be embedded
into R3, the optimal embedding equation is not solvable for {\Sigma} near the
horizon. We discuss the implications of our results in the conclusion section.
