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de Broglie-Bohm Interpretatin for Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time

Masakatsu Kenmoku·Hiroto Kubotani·Eiichi Takasugi·Yuki Yamazaki
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Abstract

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.

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Masakatsu Kenmoku, Hiroto Kubotani, Eiichi Takasugi, Yuki Yamazaki. 2000-09-21. de Broglie-Bohm Interpretatin for Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time. https://doi.org/10.1143/ptp.105.897

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