Unitarity and fuzzball complementarity: "Alice fuzzes but may not even know it!"

TL;DR

This paper analyzes the black hole information paradox through a dual lens: (i) information must be carried by every emitted quantum to preserve unitarity, challenging the idea of an information-free horizon; (ii) the fuzzball proposal replaces horizons with horizon-scale microstates, suggesting a unitary radiation process. Using qubit-based evaporation models and a tracking state, the authors show information transfer at each step, implying the horizon cannot be the Unruh vacuum if evaporation is unitary. They then examine fuzzballs and the concept of fuzzball complementarity, arguing that scale-dependent infall (E >> T_H versus E ~ T_H) can reconcile infall experiences with unitary evaporation, and that AMPS does not rule out this picture. Overall, the work supports fuzzball-based resolutions to the information paradox and clarifies how infalling observers might experience reality in a horizonless microstate framework.

Abstract

We investigate the recent black hole firewall argument. For a black hole in a typical state we argue that unitarity requires every quantum of radiation leaving the black hole to carry information about the initial state. An information-free horizon is thus inconsistent with unitary at every step of the evaporation process (in particular both before and after Page time). The required horizon-scale structure is manifest in the fuzzball proposal which provides a mechanism for holding up the structure. In this context we want to address the experience of an infalling observer and discuss the recent fuzzball complementarity proposal. Unlike black hole complementarity and observer complementarity which postulate asymptotic observers experience a hot membrane while infalling ones pass freely through the horizon, fuzzball complementarity postulates that fine-grained operators experience the details of the fuzzball microstate and coarse-grained operators experience the black hole. In particular, this implies that an infalling detector tuned to energy E ~ T, where T is the asymptotic Hawking temperature, does not experience free infall while one tuned to E >> T does.

Figures (7)

• Figure 2: (a) Two subsequent "nice slices" that smoothly intersect initial infalling matter (yellow), newly created Hawking-pairs (blue and red) at the horizon and early Hawking radiation (orange). (b) Hawking-pair creation at the horizon (dashed line) on two subsequent nice slices sufficiently far away from the singularity (zigzag line) in order to avoid large curvatures. On slice $S_1$ the outgoing member of the pair created at the horizon is labelled "$B_1$" and its ingoing partner is labelled "$C_1$". On slice $S_2$ the pair $B_1C_1$ has moved away from the horizon in opposite directions and a new pair "$B_2$" and "$C_2$" is created. When not needed, we omit the subscripts which indicate the slice on which they were created.
• Figure 3: (a) A typical quantum comes out of the system. To preserve unitarity it must carry information of the state. According to black hole complementarity it originates from a hot membrane outside the event horizon. (b) According to views held by many if such a quantum is reflected back in it will have a free infall, independent of the details of the state. This seems odd because if there is a microscopic description of the emission process one would expect the microscopic dynamics to be reversible.
• Figure 4: To answer the infall question we have to discuss the interaction of the infalling observer with the full system: radiation quanta emitted from the fuzzball either cross the potential barrier at $r_*$ or get reflected back into the fuzz. An infalling observer thus encounters a single radiation quantaumoutside the barrier but a lot of quanta partially trapped between the barrier and the fuzz. Further they encounter the fuzz itself. We refer to this region as "near-fuzz" instead of "near-horizon" to emphasize the lack of a horizon in the fuzzball picture.
• Figure 5: The extended AdS Schwarzschild black hole can be understood as the sum over entangled fuzzball solutions $|g_k \rangle_L$ and $|g_k \rangle_R$.
• Figure 6: (a) Expectation value of an operator $\hat{O}_R$ in a given fuzzball state $|\psi_g \rangle_R$. (b) For a suitably coarse-grained $\hat{O}_R$ in a typical $|\psi_g \rangle_R$, this expectation value can be approximately obtained in the eternal AdS geometry.