  Since Hawking's 1974 discovery, we expect that a black hole formed by
collapse will emit radiation and eventually disappear. Closely related to the
information loss puzzle is the challenge to define an objective notion of
physical entropy which increases throughout this process in a way consistent
with unitarity. In recent years, this has been addressed with certain notions
of coarse grained entropy. We have suggested instead that physical entropy
should be identified with 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,
notably the universe as a whole. For this to work, it would have to be that the
matter-gravity entanglement entropy of the late-time state of black hole
evaporation is larger than the entropy of the freshly formed black hole. We
argue here that this is possibly the case due to (usually neglected)
photon-graviton interactions. If black hole evaporation is slowed down by
putting the black hole in a slightly permeable box, we give plausibility
arguments that the radiation remaining after a large black hole has evaporated
will (be pure and) mainly consist of roughly equal numbers of photons and
gravitons entangled with one another -- with a photon-graviton entanglement
entropy possibly greater than the entropy of the freshly formed black hole. It
also seems possible that, even in the absence of such a box, the matter-gravity
entanglement entropy might still increase and the late-time state again be a
pure state of (predominantly) photons highly entangled with soft gravitons that
the Hawking-emitted photons themselves had radiated. More work is needed to
find out if it is indeed so.
