Hamiltonian Formalism for Black Holes and Quantization

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.

13 pages, Plain Tex, no figures, Mail Adrress: Dipartimento di Fisica Teorica dell'Universita` di Torino, Via Giuria 1, I-10125 Torino, Italy; TWO REFERENCES ADDED

Cited by in corpus (43)

• Dilaton Gravity in Two Dimensions
• Disappearance of Black Hole Singularity in Quantum Gravity
• Noncommutative Quantum Cosmology
• Area spectrum of the Schwarzschild black hole
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Noncommutative Geometry and Cosmology
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Quantum Attractor Flows
• Hamiltonian spacetime dynamics with a spherical null-dust shell
• Quantum geometrodynamics for black holes and wormholes
• Quantization of Midisuperspace Models
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Conditional Symmetries and the Canonical Quantization of Constrained Minisuperspace Actions: the Schwarzschild case
• Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity
• Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole
• Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries
• Entropy from the foam
• Quantization of the String Inspired Dilaton Gravity and the Birkhoff Theorem
• Canonical Quantization of the BTZ Black Hole using Noether Symmetries
• Decoupling of the re-parametrization degree of freedom and a generalized probability in quantum cosmology
• Quantization of the Schwarzschild black hole: a Noether symmetry approach
• On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• Multi-exponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models
• Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction
• Classical polymerization of the Schwarzschild metric
• Dimensional Reduction of Gravity and Relation between Static States, Cosmologies and Waves
• Horizons in 1+1 Dimensional Dilaton Gravity Coupled to Matter
• Towards a Supersymmetric Generalization of the Schwarzschild Black Hole
• Wheeler-DeWitt equation beyond the cosmological horizon: Annihilation to nothing, infinity avoidance, and loss of quantum coherence
• Quantum gravitational wave function for the interior of a black hole and the generalized uncertainty principle
• Group Theoretical Quantization of Schwarzschild and Taub-NUT
• Why two makes it more attractive than just with one... or Bianchi class-A models and Reissner-Nordström Black Holes in Quantum N=2 Supergravity
• Spinorial Wheeler-DeWitt wave functions inside black hole horizons
• Integrals of equations for cosmological and static reductions in generalized theories of gravity
• Quantization of the Reissner-Nordström Black Hole
• Unified description of cosmological and static solutions in affine generalized theories of gravity: vecton - scalaron duality and its applications
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
• Higher dimensional black holes as constrained systems
• Schwarzschild Mass Uncertainty
• Cyclic Kruskal Universe: a quantum-corrected Schwarzschild black hole in unitary unimodular gravity
• A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations
• On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron