Abstract
We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. We then show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement breaks down at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.
Highlights
Black holes provide an ideal theoretical laboratory for testing attempts to reconcile gravity with quantum mechanics
This is exactly the criterion used in the Papadodimas and Raju (PR) construction, and since maximal entanglement is monogamous it would imply that the operator we found agrees with the PR construction
In this paper we used the construction of local bulk observables to gain insight into the black hole interior
Summary
Black holes provide an ideal theoretical laboratory for testing attempts to reconcile gravity with quantum mechanics. We will argue that it does, in the sense that even for evaporating black holes the CFT accurately describes the geometry seen by an infalling classical observer To show this we start from the simple observation that in the presence of a horizon a bulk field can be decomposed into parts we call ingoing and outgoing. It can be represented as a state-dependent operator, using entanglement across the horizon and following the construction of Papadodimas and Raju In this sense a stable black hole has conventional internal geometry, with a hybrid description in the CFT: the ingoing part of a field can be expressed as a conventional CFT operator while the outgoing part can only be accessed using entanglement. Since the ingoing part of the field can describe an infalling classical observer, while the outgoing part of the field describes Hawking particles and is responsible for the evaporation process, this provides a mechanism for the CFT to reconcile the semiclassical behavior of an infalling observer with the breakdown of geometry required for unitary Hawking evaporation
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