Hamiltonian spacetime dynamics with a spherical null-dust shell

Jorma Louko, Bernard F. Whiting, and John L. Friedman
Phys. Rev. D 57, 2279 – Published 15 February 1998
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Abstract

We consider the Hamiltonian dynamics of spherically symmetric Einstein gravity with a thin null-dust shell, under boundary conditions that fix the evolution of the spatial hypersurfaces at the two asymptotically flat infinities of a Kruskal-like manifold. The constraints are eliminated via a Kuchař-type canonical transformation and Hamiltonian reduction. The reduced phase space Γ̃ consists of two disconnected copies of R4, each associated with one direction of the shell motion. The right-moving and left-moving test shell limits can be attached to the respective components of Γ̃ as smooth boundaries with topology R3. Choosing the right-hand-side and left-hand-side masses as configuration variables provides a global canonical chart on each component of Γ̃, and renders the Hamiltonian simple, but encodes the shell dynamics in the momenta in a convoluted way. Choosing the shell curvature radius and the “interior” mass as configuration variables renders the shell dynamics transparent in an arbitrarily specifiable stationary gauge “exterior” to the shell, but the resulting local canonical charts do not cover the three-dimensional subset of Γ̃ that corresponds to a horizon-straddling shell. When the evolution at the infinities is freed by introducing parametrization clocks, we find on the unreduced phase space a global canonical chart that completely decouples the physical degrees of freedom from the pure gauge degrees of freedom. Replacing one infinity by a flat interior leads to analogous results, but with the reduced phase space R2R2. The utility of the results for quantization is discussed.

  • Received 7 August 1997

DOI:https://doi.org/10.1103/PhysRevD.57.2279

©1998 American Physical Society

Authors & Affiliations

Jorma Louko*

  • Department of Physics, University of Maryland, College Park, Maryland 20742-4111

Bernard F. Whiting

  • Department of Physics, University of Florida, Gainesville, Florida 32611

John L. Friedman

  • Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201

  • *On leave of absence from Department of Physics, University of Helsinki. Present address: Max-Planck-Institut für Gravitations-physik, Schlaatzweg 1, D-14473 Potsdam, Germany. Electronic address: louko@aei-potsdam.mpg.de
  • Electronic address: bernard@bunyip.phys.ufl.edu
  • Electronic address: friedman@thales.phys.uwm.edu

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Issue

Vol. 57, Iss. 4 — 15 February 1998

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