Unitarity and the Hilbert space of quantum gravity

TL;DR

This paper argues that assuming unitarity and complete black hole evaporation restricts the Hilbert space of quantum gravity, excluding many semiclassical configurations, especially high-entropy states, from being physically realizable.

Contribution

It demonstrates that unitarity and evaporation assumptions impose strong constraints on the quantum states, ruling out a large class of semiclassical spacetime configurations.

Findings

High-entropy semiclassical states are excluded from the quantum gravity Hilbert space.

Unitarity and complete evaporation imply a one-to-one correspondence between asymptotic and initial states.

Many semiclassical configurations do not have quantum counterparts under these assumptions.

Abstract

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.