Singularities, Firewalls, and Complementarity

TL;DR

This paper analyzes the AMPS firewall paradox and proposes a nonstandard interpretation in which the firewall is effectively an extension of a migrating singularity that intersects the horizon at the Page time. It argues that firing at the scrambling time is not forced by conservation of entanglement and distinguishes between generic versus scrambled states, which changes expectations for firewall formation. The work emphasizes that complementarity may apply to the horizon but not to the firewall, and explores cloning, apparent horizons, and strong complementarity as potential resolutions. It also discusses the observational status for infalling observers and the need for a quantitative theory of singularity evolution.

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.

Figures (8)

• Figure 1: A small portion of an old black hole. $A$ and $B$ are points on opposite sides of the horizon that the infalling observer sees as neighboring. R is the outgoing Hawking radiation.
• Figure 2: The formation of a firewall at the Page time.
• Figure 3: The region behind the firewall does not exist. The firewall is an extension of the singularity.
• Figure 4: The same as Figure \ref{['f3']} but with the singularity smoothed and spacelike.
• Figure 5: The migration of the singularity. The black region is the part of the spacetime that is removed by the shift of the singularity from the green curve to the red curve. The blue line is a light sheet the intercepts the Hawking radiation, the horizon, and the singularity.