Note on Ashtekar's variables in the spherically symmetric case
Abstract
The reformulation of the Hamiltonian equations of gravity in threedimensional 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 3space is found to be nonRiemannian. The possible physical implications of this result are briefly considered.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 October 1988
 DOI:
 10.1088/02649381/5/10/002
 Bibcode:
 1988CQGra...5L.139B
 Keywords:

 Field Theory (Physics);
 Gravitation Theory;
 Hamiltonian Functions;
 Quantum Theory;
 Symmetry;
 Einstein Equations;
 Equations Of Motion;
 Manifolds (Mathematics);
 Schwarzschild Metric;
 SpaceTime Functions;
 Physics (General)