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Quantum mechanics of the Schwarzschild–de Sitter black hole
Phys. Rev. D 58, 024010 – Published 22 June, 1998
DOI: https://doi.org/10.1103/PhysRevD.58.024010
Abstract
In the present paper, we apply the quantum general relativity theory to the Schwarzschild–de Sitter black hole. We start by writing down the super-Hamiltonian and supermomentum constraints for general, neutral, spherically symmetric, space-times, with a positive cosmological constant. Then we solve the constraints for the canonical momenta and canonically quantize the space-time using Dirac’s formalism for constrained systems. The resulting operatorial equations are exactly solved in the WKB approximation, giving rise to a wave function. Finally, for a particular ansatz of the canonical variables, we compute the quantum mechanical density probability and show how it depends on the mass of the hole and on the cosmological constant.
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