Geometrodynamics of Schwarzschild Black Holes

Abstract

The curvature coordinates $T,R$ of a Schwarz\-schild spacetime are turned into canonical coordinates $T(r),\mathsf{R}(r)$ 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 $P_T(r),P_{\mathsf{R}}(r)$ 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 $\Psi (m;T,\mathsf{R}]=\Psi (m)$ 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.

44 pages, Latex file, UU-REL-94/3/1

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• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
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