Entanglement entropy of two spheres

We study the entanglement entropy S-AB of a massless free scalar field on two spheres A and B whose radii are R-1 and R-2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S-A;B equivalent to S-A + S-B - S-AB is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r >> R-1, R-2, where S-A and S-B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.