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Towards A Quantum Notion Of Covariance In Spherically Symmetric Loop Quantum Gravity, Rodolfo Gambini, Javier Olmedo, Jorge Pullin

Faculty Publications

The covariance of loop quantum gravity studies of spherically symmetric space-times has recently been questioned. This is a reasonable worry, given that they are formulated in terms of slicing-dependent variables. We show explicitly that the resulting space-times, obtained from Dirac observables of the quantum theory, are covariant in the usual sense of the way-they preserve the quantum line element-for any gauge that is stationary (in the exterior, if there is a horizon). The construction depends crucially on the details of the Abelianized quantization considered, the satisfaction of the quantum constraints, and the recovery of standard general relativity in the classical …