Unitarity and the Hilbert space of quantum gravity

Understand

Under the premises that physics is unitary and black hole evaporation is complete (no remnants, no topology change), there must exist a one-to-one correspondence between states on future null and timelike infinity and on any earlier spacelike Cauchy surface (e.g., slices preceding the formation of the hole).

• We show that these requirements exclude a large set of semiclassical spacetime configurations from the Hilbert space of quantum gravity.
• In particular, the highest entropy configurations, which account for almost all of the volume of semiclassical phase space, would not have quantum counterparts, i.e.
• would not correspond to allowed states in a quantum theory of gravity.