Note on Ashtekar's variables in the spherically symmetric case

Details Note on Ashtekar's variables in the spherically symmetric case Note on Ashtekar's variables in the spherically symmetric case

Oct 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5l.139b&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, Oct. 1, 1988, p. L139-L142.

Mathematics

13

Field Theory (Physics), Gravitation Theory, Hamiltonian Functions, Quantum Theory, Symmetry, Einstein Equations, Equations Of Motion, Manifolds (Mathematics), Schwarzschild Metric, Space-Time Functions

Scientific paper

The reformulation of the Hamiltonian equations of gravity in three-dimensional space proposed by Ashtekar (1987) is investigated analytically. A generalization to spherically symmetric field configurations is derived, and the solutions of the resulting geometrostatic problem are explored. The solution corresponding to the Schwarzschild solution of the conventional formulation is shown to have a gauge Lambda = 0 which is inconsistent with a Schwarzschild solution, and the associated 3-space is found to be non-Riemannian. The possible physical implications of this result are briefly considered.

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