Geometrodynamics of Schwarzschild black holes

Karel V. Kuchař
Phys. Rev. D 50, 3961 – Published 15 September 1994
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Abstract

The curvature coordinates T, R of a Schwarzschild spacetime are turned into canonical coordinates T(r), ssR(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 PT(r), PssR(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 Ψ(m;T,ssR]=Ψ(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.

  • Received 22 February 1994

DOI:https://doi.org/10.1103/PhysRevD.50.3961

©1994 American Physical Society

Authors & Affiliations

Karel V. Kuchař

  • Department of Physics, University of Utah, Salt Lake City, Utah, 84112

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Issue

Vol. 50, Iss. 6 — 15 September 1994

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