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Hamiltonian Formalism for Black Holes and Quantization

Marco Cavaglia`·Vittorio de Alfaro·Alexandre T. Filippov
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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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Marco Cavaglia`, Vittorio de Alfaro, Alexandre T. Filippov. 1994-12-06. Hamiltonian Formalism for Black Holes and Quantization. https://doi.org/10.1142/s0218271895000442

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