1993/02/18 by Riccardo Capovilla, R. Capovilla, John Dell +6
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematics and Applications #Optimization and Mathematical Programming #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9302020
15 pages, UMDGR93-140, NSF-ITP-93-20
arxiv created 1993/02/18 · openalex publication_date 1993/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non-degenerate, 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 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.