Affine quantization of the Reissner-Nordström dynamical region yields separable Wheeler-DeWitt solutions with Hermite-polynomial and Gaussian modes, plus short-distance modifications from the quantization procedure.
Geometrodynamics of Schwarzschild Black Holes
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abstract
The curvature coordinates $T,R$ of a Schwarz\-schild spacetime are turned into canonical coordinates $T(r), {\sf R}(r)$ on the phase space of spherically symmetric black holes. The entire dynamical content of the Hamiltonian theory is reduced to the constraints requiring that the momenta $P_{T}(r), P_{\sf R}(r)$ vanish. What remains is a conjugate pair of canonical variables $m$ and $p$ whose values are the same on every embedding. The coordinate $m$ is the Schwarzschild mass, and the momentum $p$ the difference of parametrization times at right and left infinities. The Dirac constraint quantization in the new representation leads to the state functional $\Psi (m; T, {\sf R}] = \Psi (m)$ which describes an unchanging superposition of black holes with different masses. The new canonical variables may be employed in the study of collapsing matter systems.
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All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.
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Affine quantization of the dynamical Reissner--Nordstr\"om region
Affine quantization of the Reissner-Nordström dynamical region yields separable Wheeler-DeWitt solutions with Hermite-polynomial and Gaussian modes, plus short-distance modifications from the quantization procedure.
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.