Firewalls in AdS/CFT

TL;DR

The paper tackles the firewall paradox by embedding it in AdS/CFT through the evaporating D1-D5-P black string, whose near-horizon region is describable by a dual CFT. It argues that after the Page time $t_{Page}$, the dual CFT is maximally entangled with early radiation and the bulk core exhibits a firewall, i.e., the dual of a thermal state is a firewall. The work also analyzes counterarguments, notably the Papadodimas-Raju proposal about coarse/fine-grained Hilbert space structure and the Harlow-Hayden assertion that firewall-detecting measurements are computationally intractable before evaporation. It further clarifies that the eternal AdS black hole is not the generic dual of a single thermal CFT and emphasizes the role of superselection sectors in determining whether a smooth infall is possible.

Abstract

Several recent papers argue against firewalls by relaxing the requirement for locality outside the stretched horizon. In the firewall argument, locality essentially serves the purpose of ensuring that the degrees of freedom required for infall are those in the proximity of the black hole and not the ones in the early radiation. We make the firewall argument sharper by utilizing the AdS/CFT framework and claim that the firewall argument essentially states that the dual to a thermal state in the CFT is a firewall.

Figures (8)

• Figure 1: In (a) a Schwarzschild black hole with the effective potential for a minimally coupled scalar is shown. The asymptotic flat space, its associated Hilbert space $\mathcal{H}_{\mathcal{A}}$ and modes living in it $\mathcal{A}$ are on the outside of the potential barrier. The near-horizon region, its associated Hilbert space $\mathcal{H}_{\mathcal{B}}$ and associated modes $\mathcal{B}$ are between the horizon and the barrier. Finally there is the region inside the horizon which is not accessible in Schwarzschild coordinates but is in Kruskal coordinates (for instance). Black hole complementarity posits that the experiences of an asymptotic and an infalling observer are complementary. The inside of the black hole is replaced by a stretched horizon for the asymptotic observer. Assuming the inside and stretched horizon Hilbert spaces to be isomorphic we denote it by $\mathcal{H}_{\mathcal{H}}$ and the associated degrees of freedom by $\mathcal{C}$. Free infall requires $\mathcal{B}$ and $\mathcal{C}$ to be maximally entangled. In (b) the firewall is shown which is supposed arise for old black holes because the entanglement structure of $\mathcal{A}$ and $\mathcal{B}$ preclude maximal entanglement between $\mathcal{B}$ and $\mathcal{C}$.
• Figure 2: The D1-D5-P black string with the effective potential barrier separating the flat space from the near horizon BTZ region. The Hilbert spaces and associated degrees of freedom have the same interpretation as in Figure \ref{['SchwarzschildGrayBody']}. For the traditional horizon with free infall, $\mathcal{B}$ and $\mathcal{C}$ have to be maximally entangled.
• Figure 3: Closed strings in a pure state hitting a stack of D-branes in (a) become open strings on the D-branes in (b). These open strings break into many lower energy open strings due to interactions on the D-branes in (c). These lower energy open strings then collide with each other and are emitted as closed strings because of the time reversal of the process (a) in (d). Since it is entropically unfavorable for all low-energy open strings to find one another at the same time so the same closed string as in (a) is not generically emitted. An effective arrow of time thus emerges.
• Figure 4: The firewall for the D1-D5-P system is shown. The argument works just like that for the Schwarzschild case. The entanglement structure between $\mathcal{A}$ and $\mathcal{B}$ required by unitarity at late times precludes the entanglement structure between $\mathcal{B}$ and $\mathcal{C}$ required for free infall. The added advantage in looking at the D1-D5-P system is that the near-horizon region is supposed to be dual to a CFT. We see that after the Page time the CFT is maximally entangled with early radiation $\mathcal{A}$.
• Figure 5: (a) The eternal AdS black hole is dual to two CFTs entangled in a certain way. An excitation on the right side representing an infalling observer requires degrees of freedom associated with the left CFT to move past the horizon. In (b) this system is realized as System 1 being in contact and thermal equilibrium with a bigger System 2.