Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-04-04
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 page, 1 figure
Scientific paper
One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one treats the state functional of the space of 3-dimensional metrics, which do not contain timelike metrics. However we can expand this state to the state which has support on the space of spacetime metrics with using additional constraint which requires the recovery of 4-dimensional quantum gravity. Enlarging the support of the state functional of the spacetime metrics, we can simply solve the usual Wheeler-DeWitt equation with the additional constraint. Using this method we can solve some unsolved problems, such as the quantization of the black hole.
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