Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition

Abstract

We recall some well and some less known results about the Kodama state and the related $\theta$ ambiguity in defining canonical variables. Based on them, we make some comments highlighting that the Kodama state for real connection variables can be given a precise meaning and that it implements a vacuum peaked on a (in a suitable sense) maximally symmetric geometry. We also highlight the similarity of this construction with the isolated horizon boundary condition $F\propto \Sigma$ and stress that it is, in agreement with earlier work, inadequate to define the notion of a quantum horizon.

6+3 pages; v2: journal version, slight shortening and added clarifications

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Cited by in corpus (6)

• Quantum gravity kinematics from extended TQFTs
• Quantum evolution of black hole initial data sets: Foundations
• An elementary introduction to loop quantum gravity
• Quantum theory of charged isolated horizons
• Quantum surface holonomies for loop quantum gravity and their application to black hole horizons
• Field dynamics on the trapping horizon in Vaidya spacetime