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The Volume Operator in Spherically Symmetric Quantum Geometry

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arxiv gr-qc/0407018 v2 pith:ZG3W7OKF submitted 2004-07-05 gr-qc

classification gr-qc
keywords sphericallysymmetricoperatorvolumehomogeneousspectrumaddsanalog
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The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Integral Hilbert spaces and the dynamics of loop quantum cosmos

    gr-qc 2026-08 conditional novelty 6.0 of 10

    In a loop quantum cosmology model with negative cosmological constant, semiclassical states built by integrating over all superselection sectors behave no differently from single-sector states, with differences below ...

  2. Orbital Dynamics and Gravitational-Wave Signatures of EMRIs in Self-Dual Loop Quantum Gravity Black Holes

    gr-qc 2026-07 reject novelty 4.0 of 10

    The paper computes EMRI orbits and waveforms in self-dual LQG black hole spacetimes and claims Fisher-matrix constraints on the quantum parameters P and a0, but the Fisher forecast uses the metric itself as the observable.

  3. Quasinormal Modes of Self-Dual Loop Quantum Gravity Corrected Kerr Black Holes

    gr-qc 2026-07 reject novelty 2.0 of 10

    In a rotating LQG-corrected black hole model, the polymeric parameter P lowers scalar quasinormal-mode frequencies, while spin raises them.

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