Matter-Gravity Entanglement Entropy and the Second law for Black Holes

Hawking showed that a black hole formed by collapse will emit radiation and eventually disappear. We address the challenge to define an objective notion of physical entropy which increases throughout this process in a way consistent with unitarity. We have suggested that (instead of coarse-grained entropy) physical entropy is matter-gravity entanglement entropy and that this may offer an explanation of entropy increase both for the black hole collapse and evaporation system and also for other closed unitarily evolving systems. For this to work, the matter-gravity entanglement entropy of the late-time state of black hole evaporation would have to be larger than the entropy of the freshly formed black hole. We argue that this may possibly be the case due to (usually neglected) photon-graviton interactions.