Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior

TL;DR

This work argues that a smooth black hole interior in AdS/CFT cannot be captured by a fixed, state-independent map from bulk to boundary; instead, interior operators must be state-dependent to preserve local EFT behind the horizon and reconcile with unitarity. The authors construct explicit state-dependent mirror operators, show their consistency under small superpositions, and extend the framework to maximally entangled (thermofield double) and more general entangled states, deriving a precise ER=EPR correspondence that depends on the entanglement structure. They address several objections, refine the equilibrium notion, and compare with other proposals (e.g., Harlow’s unitary mirrors), arguing that state-independence fails behind the horizon while the state-dependent construction remains unitary and no-signaling. The results provide a coherent picture in which the interior emerges from correlation functions in particular bases, relate to relational observables, and connect the geometry of wormholes to entanglement, with potential semi-classical explanations in Appendix. Overall, the paper strengthens the firewall–ER=EPR debate by embedding interior reconstruction in a state-dependent AdS/CFT framework with clear observational consistency for infalling observers and a natural ER=EPR interpretation for entangled systems.

Abstract

We revisit the "state-dependence" of the map that we proposed recently between bulk operators in the interior of a large AdS black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon --- not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the ER=EPR conjecture emerges from our construction in a natural and precise form. We comment on the possible semi-classical origins of state-dependence.

Figures (16)

• Figure 1: Even in the presence of a black hole, nice slices can be parameterized by coordinates on $[0,1) \times S^{d-1}$. We examine physics for a finite interval $\Delta T$ so that the future singularity is irrelevant.
• Figure 2: The relational gauge fixing proceeds in two steps: first we use intersecting geodesics to parameterize points outside the horizon. Then we use this set of points to normalize the affine parameter and follow null geodesics into the horizon.
• Figure 3: Two ways of arguing that new right movers are necessary behind a black hole horizon. Hawking's original derivation on the left, where the right movers are modes that have "bounced" off $r=0$ and propagated through the infalling matter. The analogy to the eternal black hole on the right, where the right movers come from a left asymptotic region. Both of these suffer from difficulties, and so we perform a purely local derivation leading to the same result.
• Figure 4: We derive the necessity of new modes just by demanding a regular two point function for points $P_1, P_2$ across the horizon without invoking another asymptotic region or tracing these modes back into the past.
• Figure 5: We are interested in the late-time physics of the black hole geometry, schematically denoted by the rectangular patch $P$ above.