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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We construct condensate states encoding the continuum spherically symmetric
quantum geometry of an isolated horizon in full quantum gravity, i.e. without
any classical symmetry reduction, in the group field theory formalism. Tracing
over the bulk degrees of freedom, we show how the resulting reduced density
matrix manifestly exhibits an holographic behavior. We derive a complete
orthonormal basis of eigenstates for the reduced density matrix of the horizon
and use it to compute the horizon entanglement entropy. By imposing consistency
with the isolated horizon boundary conditions and semi-classical
thermodynamical properties, we recover the Bekenstein--Hawking entropy formula
for any value of the Immirzi parameter. Our analysis supports the equivalence
between the von Neumann (entanglement) entropy interpretation and the Boltzmann
(statistical) one.
