  We consider entanglement entropy in the context of gauge/gravity duality for
conformal field theories in even dimensions. The holographic prescription due
to Ryu and Takayanagi (RT) leads to an equation describing how the entangling
surface extends into the bulk geometry. We show that setting to zero the
time-time component of the Brown-York stress tensor evaluated on the
co-dimension one entangling surface, leads to the same equation. By considering
a spherical entangling surface as an example, we observe that Euclidean action
methods in AdS/CFT will lead to the RT area functional arising as a counterterm
needed to regularize the stress tensor. We present arguments leading to a
justification for the minimal area prescription.
