Mathematics – Logic
Scientific paper
Jul 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phrvd..58b4010o&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 58, Issue 2, 15 July 1998, id. 024010
Mathematics
Logic
4
Lower Dimensional Models, Minisuperspace Models, Quantum Aspects Of Black Holes, Evaporation, Thermodynamics
Scientific paper
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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