  We argue that the entropy of a black hole is due to the entanglement of
matter fields and gravitons across the horizon. While the entanglement entropy
of the vacuum is divergent because of UV correlations, we show that low-energy
perturbations of the vacuum result in a finite change in the entanglement
entropy. The change is proportional to the energy flux through the horizon, and
equals the change in area of the event horizon divided by 4 times Newton's
constant - independently from the number and type of matter fields. The
phenomenon is local in nature and applies both to black hole horizons and to
cosmological horizons, thus providing a microscopic derivation of the
Bekenstein-Hawking area law. The physical mechanism presented relies on the
universal coupling of gravitons to the energy-momentum tensor, i.e. on the
equivalence principle.
