Aspects of the Papadodimas-Raju Proposal for the Black Hole Interior

TL;DR

The paper provides a critical examination of the Papadodimas–Raju proposal for describing the black hole interior within AdS/CFT, focusing on a small algebra of exterior observables and state-dependent mirror operators. It clarifies how bulk reconstruction can be organized at leading order in $1/N$ and discusses the extension to two-sided geometries and evaporating black holes, while highlighting deep tensions: equilibrium-state dependence implies ambiguous interior interpretations, and the proposed measurement framework cannot be realized by conventional unitary evolution. The analysis shows that while PR can curb some classic paradoxes, it introduces substantial conceptual hurdles, particularly regarding state-interpretation uniqueness and the viability of state-dependent observables under measurement, suggesting that further foundational advances are needed to make a consistent interior description. The discussion also raises questions about how quantum mechanics would apply to an infalling observer and whether new principles are required to reconcile interior reconstruction with standard quantum theory.

Abstract

In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1/N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the "state-dependence" of the proposal with more familiar phenomena, arguing that, unlike in quantum mechanics, the measurement process (including the apparatus) in something like the PR proposal or its earlier manifestations cannot be described by unitary evolution. These issues render the proposal somewhat ambiguous, and it seems new ideas would be needed to make some version of it work. I close with some brief speculation on to what extent quantum mechanics should hold for the experience of an infalling observer.

Figures (4)

• Figure 1: A one-sided AdS black hole. On the left we have the shell of matter that created the black hole in orange, the black hole interior in light blue, the horizon as a dashed line, and an infalling observer in dark blue. On the right is a detail of the region where the observer crosses the horizon, with an interesting set of modes indicated. The purple modes are easily evolved back to region I, and the green modes are already there. The red modes would need to be evolved all the way back through the collapsing shell and reflected off of $r=0$ to get them out to region I. Smoothness of the horizon requires entanglement between the red and green modes.
• Figure 2: The two-sided AdS-Schwarzschild wormhole. The infalling observer again jumps in from the right, but the red right-moving modes inside can now be understood as having come from the left side.
• Figure 3: The "method of images". We define operators in region III, but use them only to compute things which are localized above the orange shell. The expression of operators in region II in terms of the region III (and I) operators is found by using the two-sided bulk equations of motion, assuming that the shell does not exist. Of course the shell does exist, its existence can be confirmed just in region I using the ordinary AdS/CFT dictionary, and the regions below it in this figure therefore do not.
• Figure 4: The unitary process for measuring $A$ and then conditionally measuring $f$. Time goes up.