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Hamiltonian Formalism for Black Holes and Quantization
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Hamiltonian Formalism for Black Holes and Quantization
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Starting from the Lagrangian formulation of the Einstein equations for the vacuum static spherically symmetric metric, we develop a canonical formalism in the radial variable $r$ that is time--like inside the Schwarzschild horizon. The Schwarzschild mass turns out to be represented by a canonical function that commutes with the $r$--Hamiltonian. We investigate the Wheeler--DeWitt quantization and give the general representation for the solution as superposition of eigenfunctions of the mass operator.
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Cited by 1 Pith paper
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Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields
Spherically symmetric static gravity with Maxwell or massless-scalar matter exhibits Schrödinger symmetry after a canonical transformation, yielding (A)dS-Reissner-Nordström and generalized Janis-Newman-Winicour solutions.
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