Detecting Black Hole Microstates

TL;DR

This work shows that Euclidean two-point functions with carefully tuned, state-dependent probes can reveal black hole microstates in AdS via a novel gravitational saddle, the annihilation saddle, which dominates over conventional propagation saddles for appropriate probe timing. The authors corroborate the bulk mechanism with a boundary perspective based on the Eigenstate Thermalization Hypothesis, demonstrating that microstate information emerges as part of a coarse-grained ensemble description and can be extracted through a binary-search protocol over candidate shell operators. They establish robustness against ensemble fluctuations by analyzing the variance of the correlator under ETH, and they provide explicit strategies to detect microstates in both large-mass and $(2+1)$-dimensional settings. The findings suggest that microstate information for black holes may be accessible through nonperturbative Euclidean saddles, with potential implications for holographic reconstruction and the role of state-dependent observables in AdS/CFT.

Abstract

We demonstrate that the Euclidean two-point function of an appropriately chosen probe operator can detect the microstate of an asymptotically AdS black hole. This detection, which requires a tuned, state-dependent choice of probe, is the result of a new gravitational saddle, which dominates over the usual saddles. The gravitational result can be explicitly reproduced in the dual boundary CFT if we assume the eigenstate thermalization hypothesis. We also discuss a binary search protocol to detect the black hole microstate from a candidate list.

Figures (8)

• Figure 1: (a) The shell trajectory (red line) from the point of the operator insertion (red dot) on the right side of the Euclidean geometry, where we can see that the condition imposed by \ref{['eq:prep-time']} is realized. (b) The state preparation beginning with the Euclidean geometry to prepare the two copies of the CFT up until the point of time-reflection symmetry, after which we continue to Lorentzian signature, resulting in the eternal Schwarzschild-AdS black hole geometry.
• Figure 2: The gravitational saddle corresponding to $Z_1$ in \ref{['eq:normalization']}. This depicts the Euclidean disk geometries of the left and right black holes being glued along the shell trajectory.
• Figure 3: A sketch of the propagation saddle. In this saddle, the interior shell and probe do not interact with each other, so this saddle exists for any choice of the probe operator.
• Figure 4: A sketch of the annihilation saddle. In this saddle, the two probe operators in the Euclidean past and future "annihilate" the corresponding interior shell operators. This saddle only exists if the probe operator matches the interior shell operator, so it is crucial for detectability.
• Figure 5: Insertion of a light operator which does not backreact on the geometry cannot detect the black hole microstate. The resulting gravitational saddle is identical to Fig. \ref{['fig:grav-saddle']}.