Hamiltonian Formalism for Black Holes and Quantization

Details Hamiltonian Formalism for Black Holes and Quantization Hamiltonian Formalism for Black Holes and Quantization

1994-11-29

arxiv.org/abs/gr-qc/9411070v2

Int.J.Mod.Phys. D4 (1995) 661-672

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, Plain Tex, no figures, Mail Adrress: Dipartimento di Fisica Teorica dell'Universita` di Torino, Via Giuria 1, I-1012

Scientific paper

10.1142/S0218271895000442

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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