  It is known that the entanglement entropy of a scalar field, found by tracing
over its degrees of freedom inside a sphere of radius ${\cal R}$, is
proportional to the area of the sphere (and not its volume). This suggests that
the origin of black hole entropy, also proportional to its horizon area, may
lie in the entanglement between the degrees of freedom inside and outside the
horizon. We examine this proposal carefully by including excited states, to
check probable deviations from the area law.
