REVIEW
The flaw in the firewall argument
High Energy Physics - Theory · Submitted 23 Jun 2013 · 38 references
Pith's verdict: A sharp, honest defense of fuzzball complementarity that correctly shows AMPS never addressed the E>>T regime, but the load-bearing expansion of the stretched horizon is still asserted rather than derived.
T0 · AI review
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Referee report
The paper
The paper claims
The firewall argument fails, the authors argue, because it ignores how the black hole's horizon must grow to accept a falling quantum before Hawking radiation can scramble it.
The reading
What carries the argument
Three ingredients carry the argument. First, the strong-subadditivity inequality of the authors' earlier review: if physics at the horizon stays close to the local vacuum, the entanglement entropy of the radiation must keep rising by at least $ln 2 - 2epsilon$ per emitted quantum, so any resolution requires order-unity structure at the horizon, not small corrections. Second, the stretched-horizon counting argument: a surface of area $A$ already encodes $exp[S_{bek}]$ states, so a new quantum of energy $E$ cannot be placed on it without first enlarging it by an area $Delta A sim (E/m_p) ell_p^{D-2}$, giving a hemispherical bubble of radius $s_{bubble}$. Third, a gravitational-scattering estimate in the near-horizon frame, where the infalling quantum's local energy is $E r_0/s$ and the Hawking quantum's is $1/s$; the cross section $sigma sim G^2 (omega omega')^{(D-2)/2}$ gives unit interaction probability at $s_alpha$, and the black-hole-formation channel gives the same scaling. The AdS/CFT analogy — a graviton smashing on D-branes versus falling smoothly into AdS — supplies the interpretive frame for why collective fuzzball excitations could reproduce free infall.
Extended reading notes
Core claim
The central claim is that the Almheiri–Marolf–Polchinski–Sully argument does not touch the version of complementarity that a fuzzball description actually supports. The authors separate the two pictures: in traditional complementarity the Hawking modes outside the horizon are assumed identical in both descriptions ($b = b'$), whereas with fuzzballs the $E sim T$ modes are the tail end of the fuzzball structure itself and must differ ($b neq b'$), since they carry the microstate's information. What can be complementary is a hard impact by $E gg T$ quanta, which creates a large number of new, unentangled states — the count grows by a factor $e^{E/T}$. The quantitative core is a comparison of two length scales: hard scattering with Hawking radiation becomes likely only within $s_alpha sim (E/T)^{1/[2(D-2)]} ell_p$, while the stretched horizon must expand by $s_{bubble} sim (E/T)^{1/(D-2)} ell_p$ before it can absorb the new bits. Because $s_{bubble} gg s_alpha$, the infalling quantum excites the new fuzzball degrees of freedom before it is randomly scattered, so the collective excitations can still admit a smooth-infall complementary description.
Load-bearing premise
That the fuzzball surface physically expands outward to $s_{bubble} sim (E/T)^{1/(D-2)} ell_p$ before the infalling quantum arrives — an assumption the authors assert on the strength of their tunneling picture rather than derive, and which they concede leaves the complementarity map unavailable in explicit form.
Editorial extensions
If this is right
- The firewall argument is demoted from a no-go theorem to a statement about traditional complementarity, leaving fuzzball complementarity as a live option.
- Complementarity becomes an approximate, energy-graded statement: it holds for hard-impact processes with $E gg T$ and explicitly fails for the $E sim T$ Hawking quanta that carry microstate information.
- The stretched horizon is not a passive surface; it responds to an approaching quantum by expanding, so any argument that treats it as fixed until impact is mischaracterising the physics.
- Scattering off Hawking radiation does not destroy an infalling object's quantum state before it reaches the fuzzball: the transverse deflection is bounded by $ell_p (E/T)^{-1/4}$, smaller than the object's own wavelength.
- The same reasoning is proposed to apply to the Rindler decomposition of Minkowski space, where a suitable choice of Rindler frame can make the impact energy arbitrarily large and the encoding arbitrarily accurate.
Reading between the lines
- If the expansion of the stretched horizon is what saves complementarity, then the relevant physics is the dynamics of the horizon itself rather than the vacuum state near it — which suggests the debate should shift to computing that response, for example in explicit fuzzball microstates where the surface is known.
- The energy-graded character of the proposal implies a testable pattern: complementarity should improve as the ratio $E/T$ grows and as $M/m_p$ grows, so a hypothetical small black hole should show larger deviations from smooth infall than a large one.
- The D-dependence is asymmetric between the two scales — $s_{bubble}$ grows faster with $E/T$ than $s_alpha$ — so the argument gets stronger, not weaker, in higher dimensions and for heavier infalling probes; a failure would most likely appear in the opposite regime of low $E/T$ or low mass.
- If the D-brane analogy is taken seriously as more than analogy, one would expect the fuzzball's collective response to be governed by a lower-dimensional effective theory on the surface, which is a concrete target for a follow-up calculation.
Original 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.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A lot of confusion surrounds the issue of black hole complementarity, because the question has been considered without discussing the mechanism which guarantees unitarity. | gap 0.60 | 0.07 | 0.04 | asserted 1.00 |
| s1 | 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. | result 0.91 | 0.78 | 0.19 | asserted 0.99 |
| s2 | 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. | result 0.68 | 0.88 | 0.83 | asserted 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:1306.5488 by the authors.
References
How the literature uses it
48 arXiv papers cite this in 80 sentences
Papers citing it · 56 sentences without a confident label
Uses its data or values 1 paper
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In [ref] it was found that an incident wave with wavelength $λ∼R$ containing order unity number of gravitons gives $s_trapped∼l_p$.
Are there echoes of gravitational waves? · #1 · 0.82
Compares with it 2 papers
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[This picture has some affinity with the “fuzzball complementarity” scenario of [ref] in that the physics of localized jets experiencing small transverse momentum interactions applies in a regime where the jet has momentum much larger than the string tension and is thus localized inside a narrow cone, while the evolution of probes of low momentum is strongly affected by parton interactions.] To the extent that this spreading can be ignored, the center-of-mass trajectories of massless probes in localized wavepackets would reflect the causal structure of the effective geometry.
Little Strings, Long Strings, and Fuzzballs · Speculations on the black hole phase · 0.91
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Our proposal also shares some spiritual similarities with fuzzball complementarity [ref] , in which undisturbed freefall through the horizon is recovered in the limit where the incident energy of the observer is much larger than the temperature of the black hole, in the sense that local properties of the infalling observer are important to consider in both cases.
Rescuing Complementarity With Little Drama · Relation to prior works · 0.98
Cites it as support 5 papers
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In [ref] it was argued that the stretched horizon must indeed move out in advance of the particle reaching it; otherwise we violate the Bekenstein limit which says that the maximum entropy in a region is given by $S=A/4$, with $A$ the area of the stretched horizon.
A model with no firewall · The loophole in the AMPS argument · 0.98
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This corresponds to the shell transitioning into fuzzballs, and we then evade the information paradox and the associated causality problem [ref] .
Spacetime has a `thickness' · #1 · 0.97
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In [ref] it was shown that the answer to the modified firewall question is negative for standard gravitational interactions.
Can we observe fuzzballs or firewalls? · Firewall behavior · 0.96
Cites it as background 16 papers
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The form of drama envisioned in [ref] was what we might call `fiery drama,' a wall of high energy particles [ref] , though we will include in same category any strong modification of the smooth horizon geometry, including braney drama ( [ref] , but without fuzzball complementarity [ref] ), stringy drama [ref] and [ref] , or other scenarios [ref] .
Violations of the Born rule in cool state-dependent horizons · Introduction · 0.84
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This so-called "firewall" has been discussed [ref] .
Thought Experiment to resolve the Black Hole Information Paradox · Introduction · 0.89
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For more recent work see [ref] .
Unitarity and fuzzball complementarity: "Alice fuzzes but may not even know it!" · Fuzzball complementarity · 0.96
What it cites · 58 sentences without a confident label
Contests 1 paper
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For example in [ref] , it was argued that one can make $S_ent$ decrease by making small corrections to the density matrix.
An Infalling Observer in AdS/CFT · Small corrections and strong subadditivity · contest 0.85
Uses the method or tool of 1 paper
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In [ref] a method was developed, in related computation, for estimating the point where N_newN_i≳e≈2.7 .
Emission rates, the Correspondence Principle and the Information Paradox · The domain $d≲αR_s$ · 0.97
Uses data or values from 1 paper
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In [ref] the proper time between these positions was computed for different trajectories parametrized by $α≥0$, and it was found that τ_available=s̅ e^-α≤s̅
Comments on black holes I: The possibility of complementarity · Fine tuned measurements: dropping in a detector gently · 0.80
Compares with 1 paper
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This computation should be contrasted with the picture depicted in Section 5 of [ref] , where the spacelike slice is held fixed at small $r$ but evolved to later times at large $r$.]
Black Holes and Beyond · Time available for tunneling · 0.89
Cites as support 6 papers
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These state $|E_i⟩$ are fuzzball states which have a small `tail' in the region $r>2M$ corresponding to the radiation from the fuzzball [ref] .
Instability of non-supersymmetric smooth geometries · Resolution of the information paradox · 0.96
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These state $|E_i⟩$ are fuzzball states which have a small `tail' in the region $r>2M$ corresponding to the radiation from the fuzzball [ref] .
Radiation from the non-extremal fuzzball · Resolution of the information paradox · 0.96
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But there are a very large number of states $N∼Exp[S_bek]$ to tunnel to, and one finds that these small and large numbers are such that they may cancel [ref] .
How fast can a black hole release its information? · Resolution of the information paradox · 0.97
Cites as background 9 papers
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There has been a lot of interest, as well as quite some confusion, generated by a recent paper by Almheiri, Marolf, Polchinski and Sully (AMPS) [ref] on whether it is possible to smoothly fall into black holes.[ For related earlier work see [ref] , and for a more complete list of references see [ref] .]
Black Holes: Complementarity or Firewalls? · Introduction · 0.85
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There has been a lot of interest, as well as quite some confusion, generated by a recent paper by Almheiri, Marolf, Polchinski and Sully (AMPS) [ref] on whether it is possible to smoothly fall into black holes.[ For related earlier work see [ref] , and for a more complete list of references see [ref] .]
Better Late than Never: Information Retrieval from Black Holes · Introduction · 0.85
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There has been a lot of interest, as well as quite some confusion, generated by a recent paper by Almheiri, Marolf, Polchinski and Sully (AMPS) [ref] on whether it is possible to smoothly fall into black holes.[ For related earlier work see [ref] , and for a more complete list of references see [ref] .]
An Apologia for Firewalls · Introduction · 0.85
Discussion
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