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Hamiltonian Formalism for Black Holes and Quantization

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arxiv gr-qc/9411070 v2 pith:4JJVC6D5 submitted 1994-11-29 gr-qc hep-th

Marco Cavaglia` , Vittorio de Alfaro , Alexandre T. Filippov This is my paper · ORCID
classification gr-qchep-th
keywords canonicalformalismhamiltonianmassquantizationschwarzschildblackcommutes
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abstract

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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  1. Schr\"odinger Symmetry in Spherically-symmetric Static Mini-superspaces with Matter Fields

    gr-qc 2025-12 conditional novelty 7.0 of 10

    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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