Quantization of the metric diagonal spacetime with Gaussian normal coordinates
Abstract
In the analysis of the Wheeler-DeWitt equation, we have simplified the Hamiltonian constraint of the Wheeler-DeWitt equation using the coordinate transformation. The coordinate is choose such that metric becomes diagonal and as Gaussian normal coordinate. Or we treat small universe so that the metric become diagonal and universe is covered by Gaussian normal coordinates. We have solved the Wheeler-DeWitt equation of such universes. Such that universe contains Biancki I type universe or the black hole universe.
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