Quantization of static space-times

Details Quantization of static space-times Quantization of static space-times

2001-08-02

arxiv.org/abs/gr-qc/0108004v2

Phys.Rev. D65 (2002) 064012

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, made a few modifications, added Journal-ref

Scientific paper

10.1103/PhysRevD.65.064012

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum theory which actually describes quantized static space-times. The Kinematical Hilbert space is the product of the Hilbert space of gravity with that of imaginary scalar fields. It turns out that the Hamiltonian constraint of the 2+1 model corresponds to a densely defined operator in the underlying Hilbert space, and hence it is finite without renormalization. As a new point of view, this quantized model might shed some light on a few physical problems concerning quantum gravity.

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