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Since Hawking's 1974 discovery, we expect that a black hole formed bycollapse will emit radiation and eventually disappear. Closely related to theinformation loss puzzle is the challenge to define an objective notion ofphysical entropy which increases throughout this process in a way consistentwith unitarity. In recent years, this has been addressed with certain notionsof coarse grained entropy. We have suggested instead that physical entropyshould be identified with matter-gravity entanglement entropy and that this mayoffer an explanation of entropy increase both for the black hole collapse andevaporation system and also for other closed unitarily evolving systems,notably the universe as a whole. For this to work, it would have to be that thematter-gravity entanglement entropy of the late-time state of black holeevaporation is larger than the entropy of the freshly formed black hole. Weargue here that this is possibly the case due to (usually neglected)photon-graviton interactions. If black hole evaporation is slowed down byputting the black hole in a slightly permeable box, we give plausibilityarguments that the radiation remaining after a large black hole has evaporatedwill (be pure and) mainly consist of roughly equal numbers of photons andgravitons entangled with one another -- with a photon-graviton entanglemententropy possibly greater than the entropy of the freshly formed black hole. Italso seems possible that, even in the absence of such a box, the matter-gravityentanglement entropy might still increase and the late-time state again be apure state of (predominantly) photons highly entangled with soft gravitons thatthe Hawking-emitted photons themselves had radiated. More work is needed tofind out if it is indeed so.

The black hole information loss puzzle, matter-gravity entanglement entropy and the second law