Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-06-16
Prog.Theor.Phys.105:897-914,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, REVTeX; abstract and content revised
Scientific paper
10.1143/PTP.105.897
We discuss the implications of a wave function for quantum gravity, which involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the Wheeler-DeWitt equation for spherically symmetric space-time with the coordinate system arbitrary. The de Broglie-Bohm interpretation of quantum mechanics is applied to the wave function. In this interpretation, deterministic dynamics can be yielded from a wave function in fully quantum regions as well as in semiclassical ones. By introducing a coordinate system additionally, we obtain a cosmological black hole picture in compensation for the loss of general covariance. Our analysis shows that the de Broglie-Bohm interpretation gives quantum gravity an appropriate prescription to introduce coordinate systems naturally and extract information from a wave function as a result of breaking general covariance.
Kenmoku Masakatsu
KUBOTANI Hiroto
Takasugi Eiichi
Yamazaki Yuki
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