Evaporating Firewalls

TL;DR

The paper investigates whether firewalls can evaporate in AdS/CFT by coupling a black-hole CFT to an auxiliary radiation system. It argues that large AdS black hole microstates in a single CFT tend to have firewall/fuzzball structure, with no universal behind-horizon region. However, by evolving a two-CFT system to the thermofield double state, the dual geometry can include a smooth behind-horizon region, illustrating an evaporation of the firewall in a specially tuned setup. The work discusses the general case of typical two-CFT states and shows that, absent fine-tuning, the existence of a smooth horizon is not guaranteed and firewall-like behavior may persist; it also comments on related proposals like Papadodimas-Raju and fuzzball complementarity. Overall, it provides a concrete realization of Maldacena-Susskind's entanglement-based perspective on behind-horizon geometry, clarifying the role of entanglement in firewall physics and the limits of state-dependent interior reconstructions.

Abstract

In this note, we begin by reviewing an argument (independent from 1304.6483) that the large AdS black holes dual to typical high-energy pure states of a single holographic CFT must have some structure at the horizon (i.e. a firewall/fuzzball). By weakly coupling the CFT to an auxiliary system, such a black hole can be made to evaporate. In a case where the auxiliary system is a second identical CFT, it is possible (for specific initial states) that the system evolves to precisely the thermofield double state as the original black hole evaporates. In this case, the dual geometry should include the "late-time" part of the eternal AdS black hole spacetime which includes smooth spacetime behind the horizon of the original black hole. Thus, we can say that the firewall evaporates. This provides a specific realization of the recent ideas of Maldacena and Susskind that the existence of smooth spacetime behind the horizon of an evaporating black hole can be enabled by maximal entanglement with a Hawking radiation system (in our case the second CFT) rather than prevented by it. For initial states which are not finely-tuned to produce the thermofield double state, the question of whether a late-time infalling observer experiences a firewall translates to a question about the gravity dual of a typical high-energy state of a two-CFT system.

Figures (8)

• Figure 1: Proposed relation between spacetime structure and entanglement structure Czech:2012be. Density matrices for complementary sets of fundamental degrees of freedom $A$ and $B$ determine physics in the left and right wedges formed by light sheets from an extremal surface $W$. Physics in the upper and lower regions is encoded in the entanglement between $A$ and $B$. If this entanglement is removed by placing $A$ and $B$ in typical pure states in the ensembles $\rho_A$ and $\rho_B$, the right and left wedges are almost unchanged while the upper and lower regions are excised. Thus, the left and right wedges are connected by entanglement, while disentangling leaves disconnected wedges ending in a firewall.
• Figure 2: Gravity dual of state $(U \otimes {\hbox{1} \hbox{1}})|\Psi_{TD} \rangle$ for unitary $U$ close to the identity. Perturbations originating in the second asymptotic region propagate past the horizon. For general perturbations, only the exterior of the black hole in the first asymptotic region (on the right) is unaffected.
• Figure 3: CFT picture: When CFTs are weakly coupled, the product state evolves to a highly entangled state.
• Figure 4: Gravity dual $M'$ of a state $|\Psi'(t) \rangle$ that is the vacuum state before time $T$ but changes after time $T$ due to a perturbation of the Hamiltonian. The spacetime $M'$ matches pure global AdS in the past of the future light sheet from the boundary surface at time $T$ (shaded).
• Figure 5: Gravity dual of a state of a two-CFT system where the two CFTs are coupled between time $T$ and $T'$. Before time $T$ and after time $T'$, the CFT states are identical to states with known dual geometries.