The flaw in the firewall argument

TL;DR

This work argues that the AMPS firewall result does not rule out a viable resolution to the black hole information paradox. By invoking the fuzzball construction in string theory, the authors posit real horizon degrees of freedom that replace the traditional horizon, with a complementary description emerging for high-energy infalling quanta when $E\gg T$. The key mechanism is horizon expansion, quantified by $s_{bubble}$, which allows a large set of unentangled fuzzball states to be accessed before scattering with near-horizon Hawking quanta at distance $s_{\alpha}$, thereby enabling a dual description akin to AdS/CFT for hard-impact processes. This framework preserves unitarity while maintaining effective field theory for appropriate (high-energy) measurements and clarifies how information can be radiated without a firewall.

Abstract

A lot of confusion surrounds the issue of black hole complementarity, because the question has been considered without discussing the mechanism which guarantees unitarity. Considering such a mechanism leads to the following: (1) The Hawking quanta with energy E of order the black hole temperature T carry information, and so only appropriate processes involving E>>T quanta can have any possible complementary description with an information-free horizon; (2) The stretched horizon describes all possible black hole states with a given mass M, and it must expand out to a distance s_{bubble} before it can accept additional infalling bits; (3) The Hawking radiation has a specific low temperature T, and infalling quanta interact significantly with it only within a distance s_{alpha} of the horizon. One finds s_{alpha} << s_{bubble} for E>>T, and this removes the argument against complementarity recently made by Almheiri et al. In particular, the condition E>>T leads to the notion of 'fuzzball complementarity', where the modes around the horizon are indeed correctly entangled in the complementary picture to give the vacuum.

Figures (13)

• Figure 1: (a) Probing the fuzzball with hard-impact, $E\gg T$ operators causes collective excitations of the fuzzball surface. (b) The corresponding correlators are reproduced in a thermodynamic approximation by the traditional black hole geometry, where we have no fuzzball structure but we use the geometry on both sides of the horizon.
• Figure 2: (a) A graviton incident on a stack of D-branes (b) The graviton 'smashes' on the branes, converting its energy into a very special state of gluons (collective excitation) (c) The incident graviton in the dual AdS description (d) The graviton passes smoothly through the location where it had appeared to 'smash' in the brane description.
• Figure 3: The instability of 'outgoing geodesics' at the horizon. The horizontal axis is the radial coordinate, and the vertical axis is an Eddington-Finkelstein coordinate. A null geodesic at $r=2M$ headed radially outwards stays stuck at $r=2M$, one slightly outside escapes to infinity while one slightly inside falls to $r=0$.
• Figure 4: (a) Traditionally, it was assumed that in the black hole geometry the compact directions would appear as a trivial tensor product with the 3+1 metric. (b) In the actual microstates in string theory the compact directions pinch off to make KK monopoles/antimonopoles just outside the place where the horizon would have been. (c) The resulting solutions are 'fuzzballs', which have no horizon or 'interior'.
• Figure 5: Hawking radiation is just the tail end of the fuzzball structure that ends the geometry outside the horizon; thus there is no natural split between the degrees of freedom on the 'stretched horizon' and the degrees of freedom in the Hawking radiation.