Abstract
We start from the classical Hamiltonian constraint of general relativity to obtain the Einstein–Hamiltonian–Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schrödinger equation. Using a semiclassical approximation we obtain an equation for quantum gravity in Schrödinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler–DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler–DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.
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Biswas, S., Shaw, A., Modak, B. et al. Quantum Gravity Equation In Schrödinger Form In Minisuperspace Description. General Relativity and Gravitation 32, 2167–2187 (2000). https://doi.org/10.1023/A:1001902620253
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DOI: https://doi.org/10.1023/A:1001902620253