The black hole information paradox is one of the important
questions of physics in the last few decades. We study the reconstruction of
the bulk operators in AdS/CFT when the geometry contains a black hole. The
black hole exterior can be mapped to the CFT via a very simple Petz map which
coincides with the HKLL map reconstruction of the black hole exterior. For the
interior modes of the bulk theory, using the definition of the Petz recovery
channel in modular theory, we can find the mapping from the black hole interior
to the dual boundary theory. In the case of the evaporating black hole, it is
expected that the interior modes map to some operators that have support only
on the bath system, the cavity that absorbs the Hawking radiation. The most
important observation that we have here is that in the case that we have a
typical black hole microstate in the bulk, the CFT dual of the interior modes
that we can find using the Petz recovery channel are exactly the operators that
so-called "mirror operator " in the Papadodimas-Raju proposal. The
main idea of the PR proposal is to focus on a code subspace of the CFT theory,
which is created by acting with a small algebra on the corresponding pure state
and then fnd the CFT description of the interior operator in a state-dependent
manner just in the chosen code subs. Therefore, we can interpret Papadodimas-
Raju proposal as an example of the Petz map reconstruction. It may help us
answer some open questions about their procedure.
Author(s) Details
Niloofar Vardian
SISSA, via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste,
via Valerio 2, 34127 Trieste, Italy.
Please see the link:- https://doi.org/10.9734/bpi/crpps/v2/356
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