Black holes, information, and Hilbert space for quantum gravity

Abstract

A coarse-grained description for the formation and evaporation of a black hole is given within the framework of a unitary theory of quantum gravity preserving locality, without dropping the information that manifests as macroscopic properties of the state at late times. The resulting picture depends strongly on the reference frame one chooses to describe the process. In one description based on a reference frame in which the reference point stays outside the black hole horizon for sufficiently long time, a late black hole state becomes a superposition of black holes in different locations and with different spins, even if the back hole is formed from collapsing matter that had a well-defined classical configuration with no angular momentum. The information about the initial state is partly encoded in relative coefficients---especially phases---of the terms representing macroscopically different geometries. In another description in which the reference point enters into the black hole horizon at late times, an $S$-matrix description in the asymptotically Minkowski spacetime is not applicable, but it still allows for an ``$S$-matrix'' description in the full quantum gravitational Hilbert space including singularity states. Relations between different descriptions are given by unitary transformations acting on the full Hilbert space, and they in general involve superpositions of ``distant'' and ``infalling'' descriptions. Despite the intrinsically quantum mechanical nature of the black hole state, measurements performed by a classical physical observer are consistent with those implied by general relativity. In particular, the recently-considered firewall phenomenon can occur only for an exponentially fine-tuned (and intrinsically quantum mechanical) initial state, analogous to an entropy decreasing process in a system with large degrees of freedom.