Comments on black holes I: The possibility of complementarity

TL;DR

The paper critiques the AMPS firewall argument by focusing on fuzzball complementarity, which posits real horizon-scale degrees of freedom that radiate unitarily and encode information. It shows that measurements outside the horizon are inherently limited by detector time, making vacuum fluctuations indistinguishable from stretched-horizon quanta for $E \gg kT$ processes only within a short crossing-time window, and that the AdS/CFT analogy illustrates a complementary description for hard-impact events. The central claim is that a robust, approximate interior description can emerge from fuzzball dynamics for high-energy infall, while information is carried by the fuzzball surface radiation, thereby resolving the information paradox without invoking a firewall. The results have implications for how we understand black hole microstates, horizon structure, and the viability of complementarity as a resolution to the information problem, with potential testable distinctions tied to Planck-scale horizon physics and radiation spectra.

Abstract

We comment on a recent paper of Almheiri, Marolf, Polchinski and Sully who argue against black hole complementarity based on the claim that an infalling observer 'burns' as he approaches the horizon. We show that in fact measurements made by an infalling observer outside the horizon are statistically identical for the cases of vacuum at the horizon and radiation emerging from a stretched horizon. This forces us to follow the dynamics all the way to the horizon, where we need to know the details of Planck scale physics. We note that in string theory the fuzzball structure of microstates does not give any place to 'continue through' this Planck regime. AMPS argue that interactions near the horizon preclude traditional complementarity. But the conjecture of 'fuzzball complementarity' works in the opposite way: the infalling quantum is absorbed by the fuzzball surface, and it is the resulting dynamics that is conjectured to admit a complementary description.

Figures (6)

• Figure 1: (a) The traditional black hole; small corrections at the horizon cannot get information out in the Hawking radiation. (b) The fuzzball picture of black hole microstates; spacetime ends in stringy theory sources just before the horizon is reached.
• Figure 2: AdS/CFT duality, traditional complementarity and fuzzball complementarity.
• Figure 3: (a) An inertial detector in Minkowski space, making a measurement using only the indicated part of its trajectory. Vacuum fluctuations excite the detector. (b) A similar detection, but for case of a warm body radiating into the right Rindler wedge. The wavelength of quanta is of the same order as the distance from the horizon. (c) Radiation from a 'hot' body, where the wavelength is much shorter than the distance from the horizon.
• Figure 4: (a) The growth of entanglement entropy for the traditional black hole in the leading order Hawking computation (solid line), and with small corrections allowed (dashed line). (b) The entanglement entropy expected for a normal body page; $S_{ent}$ must return to zero when the body radiates away completely.
• Figure 5: (a) Creation of entangled pairs in the leading order Hawking computation. (b) Small corrections; if these could reproduce the graph Fig. \ref{['fz9']}(b) then we would not need a firewall. (c) A firewall that one can pass through; now one can detect the quanta near the horizon. (d) In a fuzzball spacetime ends before the horizon. Hawking radiation is an integral part of the dynamics of the fuzzball.