[Paper Review] Singularities, Firewalls, and Complementarity

Leonard Susskind|arXiv (Cornell University)|Aug 16, 2012

Black Holes and Theoretical PhysicsPhysics and Astronomy12 references50 citations

TL;DR

This paper reinterprets the firewall paradox in black hole physics by arguing that firewalls arise not from a breakdown of the horizon, but from the migration of the black hole's singularity toward the horizon due to growing entanglement with Hawking radiation, culminating in a collision at the Page time. The key contribution is that complementarity applies to the horizon, not the firewall, and firewalls are a consequence of non-standard singularities rather than a violation of quantum gravity principles.

ABSTRACT

Almheiri, Marolf, Polchinski, and Sully, recently claimed that once a black hole has radiated more than half its initial entropy (the Page time), the horizon is replaced by a "firewall" at which infalling observers burn up, in apparent violation of the equivalence principle and the postulates of black hole complementarity. In this paper I review the arguments for firewalls, and give a slightly different interpretation of them. According to this interpretation the horizon has standard properties, but the singularity is non-standard. The growing entanglement of the black hole with Hawking radiation causes the singularity to migrate toward the horizon, and eventually intersect it at the page time. The resulting collision of the singularity with the horizon leads to the firewall. Complementarity applies to the horizon and not to the singular firewall. Almheiri, Marolf, Polchinski, and Sully conjecture that firewalls form much earlier then the Page time; namely at the scrambling time. I argue that there is no reason to believe this generalization, and good reason to think it is wrong. For most of this paper I will assume that the firewall argument is correct. In the last section before the conclusion I will describe reasons for having reservations.

Motivation & Objective

• To resolve the apparent conflict between black hole complementarity and the firewall proposal by reinterpreting the firewall as a consequence of singularity dynamics.
• To argue that firewalls form not at the scrambling time but at the Page time, based on entanglement growth between the black hole and Hawking radiation.
• To challenge the claim that firewalls form at the scrambling time, asserting that this time scale does not reflect global typicality of quantum states.
• To explore whether firewalls are observable to infalling observers and how complementarity applies in the presence of firewalls.
• To assess the viability of strong complementarity as an alternative to firewalls, particularly in light of non-communication loopholes in entanglement measurement.

Proposed method

• Analyzes the entanglement structure between Hawking radiation (R), the black hole interior (B), and infalling matter (A) using a three-spin system model to illustrate the monogamy of entanglement.
• Applies the Page time argument to determine when the black hole's entanglement with radiation becomes maximal, leading to a breakdown of the original complementarity postulates.
• Models the singularity's evolution as it migrates toward the horizon due to increasing entanglement, culminating in a collision at the Page time.
• Distinguishes between true horizons (classical, global) and apparent horizons (local, dynamic), arguing that firewalls form at the apparent horizon.
• Evaluates the scrambling time as insufficient to establish typicality of the full quantum state, especially for global observables like firewall existence.
• Considers the Bousso-Harlow framework of strong complementarity as a potential alternative, where conflicting descriptions are non-communicable and thus not contradictory.

Experimental results

Research questions

• RQ1 At what time scale does the singularity migrate to the horizon, and what physical mechanism drives this migration?
• RQ2 Why is the firewall not detectable by an infalling observer before crossing the horizon, despite being a physical feature of spacetime?
• RQ3 Is the firewall formation at the scrambling time physically justified, or is the Page time a more accurate timescale for its emergence?
• RQ4 Can strong complementarity, as proposed by Bousso and Harlow, serve as a viable alternative to firewalls without violating quantum mechanics?
• RQ5 How does the distinction between true and apparent horizons affect the interpretation of firewall formation and the validity of complementarity?

Key findings

• The firewall is not a feature of the horizon but results from the collision of the horizon with a singularity that has migrated inward due to entanglement growth with Hawking radiation.
• Firewalls form at the Page time, not the scrambling time, because the latter does not ensure typicality of global quantum observables such as the existence of a firewall.
• Infalling observers cannot detect the firewall before crossing the horizon unless they perform fine-grained measurements on Hawking radiation outside the black hole.
• Complementarity remains valid for the horizon, but not for the firewall, which is a distinct physical entity arising from non-standard singularity dynamics.
• The argument against early firewall formation at the scrambling time rests on the fact that scrambling time only ensures typicality of small subsystems, not global properties.
• The Bousso-Harlow strong complementarity proposal remains viable as a potential resolution, provided no experiment can be constructed to communicate a contradiction between observers about entanglement.