The Initial Value Problem in Light of Ashtekar's Variables [chapter]

R. Capovilla, J. Dell, T. Jacobson, B. L. Hu, T. A. Jacobson
Directions in General Relativity  
The form of the initial value constraints in Ashtekar's hamiltonian formulation of general relativity is recalled, and the problem of solving them is compared with that in the traditional metric variables. It is shown how the general solution of the four diffeomorphism constraints can be obtained algebraically provided the curvature is nondegenerate, and the form of the remaining (Gauss law) constraints is discussed. The method is extended to cover the case when matter is included, using an
more » ... luded, using an approach due to Thiemann. The application of the method to vacuum Bianchi models is given. The paper concludes with a brief discussion of alternative approaches to the initial value problem in the Ashtekar formulation.
doi:10.1017/cbo9780511524653.008 fatcat:jqmrzcuc3rfbfksn35qzhra3zu