Group Theoretical Quantization of Schwarzschild and Taub-NUT

Abstract

Stationary spherically symmetric gravity is equivalent to a nonlinear coset sigma model on SL(2,R)/SO(2) coupled to a gravitational remnant. Classically there are stationary solutions besides the static Schwarzschild metric labeled by the Schwarzschild mass $m$ and the Taub-NUT charge $l$. Imposing the SL(2,R) symmetry at the quantum level the Wheeler-DeWitt equation becomes related to the Casimir operator on the coset, which makes the system amenable to exact quantization.

7 pages, LaTex, accepted for publication in Phys. Lett. B

References in corpus (6)

• Geometrodynamics of Schwarzschild Black Holes
• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Hamiltonian Formalism for Black Holes and Quantization
• Hamiltonian quantization of General Relativity with the change of signature
• Reduced SL(2,R) WZNW Quantum Mechanics

Cited by in corpus (4)

• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Quantum Attractor Flows
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
• Quantization of the Reissner-Nordström Black Hole