[Paper Review] Firewall or smooth horizon?

Amos Ori|arXiv (Cornell University)|Aug 31, 2012

Black Holes and Theoretical Physics19 references14 citations

TL;DR

This paper argues that if semiclassical gravity and the equivalence principle hold throughout the evaporation process, then most black hole information remains trapped inside the black hole during the semiclassical phase, avoiding the firewall paradox. Instead of information being carried out by Hawking radiation, the horizon remains smooth and regular, with information potentially released later via a long-lived remnant or slow emission, resolving the AMPS paradox without requiring firewalls.

ABSTRACT

Recently, Almheiri, Marolf, Polchinski, and Sully found that for a sufficiently old black hole (BH), the set of assumptions known as the \emph{complementarity postulates} appears to be inconsistent with the assumption of local regularity at the horizon. They concluded that the horizon of an old BH is likely to be the locus of local irregularity, a "firewall". Here I point out that if one adopts a different assumption, namely that semiclassical physics holds throughout its anticipated domain of validity, then no inconsistency seems to arise, and the horizon retains its regularity. In this alternative view-point, the vast portion of the original BH information remains trapped inside the BH throughout the semiclassical domain of evaporation, and possibly leaks out later on. This appears to be an inevitable outcome of semiclassical gravity.

Motivation & Objective

• To resolve the firewall paradox proposed by AMPS by challenging the assumption that information is efficiently carried out by Hawking radiation during semiclassical evaporation.
• To argue that the standard complementarity postulates, particularly the idea that information is radiated away early, are inconsistent with the assumption that semiclassical physics holds throughout its domain of validity.
• To demonstrate that a smooth horizon is consistent with unitarity and information conservation if the majority of information is stored within the black hole interior.
• To explore the geometric and thermodynamic properties of spacelike hypersurfaces intersecting the horizon at small mass, showing large internal volumes capable of storing information.
• To propose that information is released only after the black hole reaches Planck-scale mass, possibly via a finite-lifetime remnant or slow emission of low-frequency particles.

Proposed method

• Adopt the 'semiclassicality postulate': semiclassical gravity and the equivalence principle are assumed valid as long as curvature remains sub-Planckian.
• Use Bekenstein-Hawking entropy $ S = 4\pi m^2 $ as a measure of information capacity, but argue it does not bound the information content of an evaporating black hole.
• Analyze the geometry of spacelike hypersurfaces $ \Sigma $ that intersect the horizon at small mass $ m \ll M_0 $, showing a narrow throat but large internal volume $ \sim M_0^3 $, capable of storing vast information.
• Model the black hole mass evolution as $ m(v) = c(t_0 - v)^{1/3} $, with $ t_0 \sim M_0^3 $, to describe the semiclassical evaporation phase.
• Contrast this scenario with the standard 'information-at-horizon' picture (Option A), showing that Option B—information stored inside—avoids the AMPS contradiction.
• Consider the fate of information after evaporation, proposing a finite-lifetime remnant with mass $ m_{\text{rem}} \sim m_p $ that slowly emits information via low-frequency particles.

Experimental results

Research questions

• RQ1 Can the firewall paradox be avoided if we assume that semiclassical gravity holds throughout its domain of validity, rather than assuming information is radiated early?
• RQ2 What is the maximum information capacity of a black hole with remaining mass $ m $, and how does it compare to the initial information content $ S(M_0) = 4\pi M_0^2 $?
• RQ3 Is it possible for a black hole with small mass $ m \ll m_p $ to still possess a large internal volume capable of storing information, even as the throat shrinks?
• RQ4 Does the assumption that most information remains inside the black hole during evaporation resolve the inconsistency in the AMPS argument?
• RQ5 What are the implications of this scenario for the final state of black hole evaporation, particularly regarding the formation of a remnant or slow emission of information?

Key findings

• The assumption that information is carried out by Hawking radiation during the semiclassical phase leads to a contradiction with local regularity at the horizon, as shown by AMPS.
• If instead the semiclassical theory of gravity is assumed to hold throughout its domain (including sub-Planckian curvature), no contradiction arises, and the horizon remains smooth.
• The internal volume of a spacelike hypersurface intersecting the horizon at small mass $ m $ is large, scaling as $ \sim M_0^3 $, and can store information even when $ m \ll m_p $.
• The information content of the black hole is not bounded by $ S(m) = 4\pi m^2 $, but rather by the initial entropy $ S(M_0) = 4\pi M_0^2 $, implying most information remains inside.
• A finite-lifetime remnant with mass $ m_{\text{rem}} \sim m_p $ is a viable candidate for storing and slowly releasing information, with emission rates of order $ M_0^{-2} $.
• This scenario avoids firewalls and preserves unitarity, provided that the semiclassical theory is valid up to the Planck scale, even if it conflicts with some AdS/CFT expectations.