No Holography for Eternal AdS Black Holes

TL;DR

The paper argues that the eternal AdS black hole is not dual to two decoupled CFTs in a thermofield double state, because the bulk requires left–right interactions across the horizon, which the boundary theories lack. Through a toy model, Rindler-AdS analyses, and BTZ/orbifold considerations, it shows that entanglement alone does not guarantee spacetime connectivity and that hyperbolic CFTs capturing wedge physics cannot reproduce horizon-crossing physics when the boundary is reduced to cylinders. The authors conclude that the correct dual geometries resemble the exterior of the black hole outside the stretched horizon, capping off before the global horizon, with the UV completion potentially realized by fuzzball microstates. These results challenge ER=EPR and entanglement=spacetime naively and suggest a need for boundary interactions or alternative bulk topologies to describe connected bulk regions.

Abstract

It is generally believed that the eternal AdS black hole is dual to two conformal field theories with compact spatial sections that are together in a thermofield double state. We argue that this proposal is incorrect, and by extension so are the "entanglement=geometry" proposal of Van Raamsdonk and "ER=EPR" proposal of Maldacena and Susskind. We show that in the bulk there is an interaction needed between the two halves of the Hilbert space for connectivity across the horizon; however, there is no such interaction between the CFTs. This rules out the possibility of the dual to the CFTs being the eternal AdS black hole. We argue the correct dual "geometries" resemble the exterior of the black hole outside the stretched horizon but cap off before the global horizon. This disallows the possibility of a shared future (and past) wedge where Alice falling from one side can meet Bob falling from the other. We expect that in the UV complete theory the aforementioned caps will be fuzzballs.

Figures (5)

• Figure 1: In \ref{['fig:Ttt']}, $T_{tt}$ is plotted at time $t<L/2$ after the insertion of the mirror. We cut off the sums at $m,n=30$ in Equation \ref{['eq:Ttt']}. The left pulse is created at the mirror ($x=0$) and propagates away along the lightcone. Note that box wall is at $x=L/2$. The pulse at $x=L-t$ is actually the left-moving bounced pulse that only enters the physical region once the pulse leaving the quench site at $x=0$ hits the wall. In \ref{['fig:acc-obs']}, an accelerated observer escapes the divergent stress-tensor, and does not notice that a mirror was inserted.
• Figure 2: Global AdS can be "Rindlerized". In (a) the associated acceleration horizons and closed string Bulk-Alice falling through one of them is shown. In (b) the associated causal diamonds and open string Boundary-Alice escaping it is shown.
• Figure 3: In (a) the effect of orbifolding in the bulk is shown. Connectivity across the horizon is maintained and thus so is the interaction. In (b) the effect of orbifolding on the boundary is shown. Hyperbolic CFTs are replaced by cylindrical ones which are not connected and do not interact.
• Figure 5: The idea advocated in Czech:2012be, based on the proposal of Maldacena:2001kr, (a) is that generic geometric-microstates dual to decoupled CFTs resemble a black hole outside the stretched horizon but then differ sharply. However, the thermofield double state would involve a topology change in the bulk which creates an eternal AdS black hole. Alice and Bob falling from different sides can then meet in the future wedge. In (b) we summarise our results which is that for all kinds of generic states including the thermofield double state there is no forward wedge. The wedges end in fuzzballs, which maybe thought of as a microscopic realisation of the stretched horizon. Alice and Bob falling on the two sides thermalise on the fuzz but do not meet each other.
• Figure 6: An accelerating observer only intersects the modes of the right wedge so can only do non-Bell measurements. These do not measure the actual state of the system but instead collapse the system into a different state. An inertial observer on the other hand intersects both modes and thus can perform a Bell measurement to verify that the full state is the Minkowski vacuum.