Abstract
In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. We also calculate holographic complexity for the d = 2 ETW geometries, finding that complexity-action and complexity-volume proposals give the same linear growth at late times, but differ at early times.A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.
Highlights
The AdS/CFT correspondence is believed to provide a non-perturbative description of quantum gravity for spacetimes which are asymptotic to Anti-de Sitter space
In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-ofthe-world (ETW) brane
The horizon is not distinguished by any local physics, so a conventional expectation is that black hole microstate geometries should include at least some of the behind-the-horizon region from the maximally extended geometry
Summary
The AdS/CFT correspondence is believed to provide a non-perturbative description of quantum gravity for spacetimes which are asymptotic to Anti-de Sitter space. Whether or not we have an effective four-dimensional description for physics in the second asymptotic region will depend on the details of the microstate geometry, in particular on the size of the black hole relative to the AdS scale and to the ETW brane trajectory These in turn depend on the details of the state we are considering. If there exist states for which the conditions for localized gravity are realized, the effective description of the physics beyond the black hole horizon would correspond to d-dimensional FRW cosmology, where the evolution of the scale factor corresponds to the evolution of the proper size of the ETW brane in the full geometry This evolution corresponds to an expanding and contracting FRW spacetime which classically starts with a big bang and ends with a big crunch, though we expect that the early and late time physics does not have a good d-dimensional description.
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