Entanglement entropy due to near-horizon degrees of freedom

Assuming that the dominant contribution to the entropy due to entanglement across a spherical hypersurface comes from the near-horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski spacetime across a spherical entangling surface. The resulting entanglement entropy is found to be proportional to the entangling surface as expected. A logarithmic subleading term with positive coefficient is also found through numerical computation. We have extended the analysis to higher dimensions as well.