Black holes, quantum information, and unitary evolution

The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and, in particular, unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with minimal departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert-space approach an apparently coarser form of localization can be described in terms of tensor decompositions of the Hilbert space of the complete system. This suggests a general framework in which to seek a consistent description of quantum gravity, and approximate emergence of spacetime. Other possible aspects of such a framework—in particular, symmetries—are briefly discussed.

Figure 1

A schematic of factorization of a large Hilbert space into tensor factors. Intersections correspond to common factors of the overlapping Hilbert spaces.

Figure 2

A Kruskal diagram for a black hole. Also shown is matter infalling in the far past; if the black hole formed from this matter, the vacuum geometry below it, including $X+\le 0$, is not present.

Figure 3

A black hole pictured in Eddington-Finkelstein coordinates, together with a family of nice slices, and schematic representation of production/evolution of paired Hawking excitations.

Figure 4

A sketch of the growth of the von Neumann entropy of the external state resulting from Hawking evolution, as compared to its ultimate decline (here pictured as beginning near the half life of the black hole) necessary for unitary evolution.

Figure 5

Sketch of possible evolution of a massive remnant or fuzzball, in the Eddington-Finkelstein geometry of Fig. 3. An infalling observer following the arrow is expected to be disrupted upon impacting the surface.