1998/11/25 by J. Demaret, Jacques Demaret, Laurent Querella +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #nlin.SI #solv-int
paper · pdf · doi:10.1088/0264-9381/16/3/009
published as Class.Quant.Grav. 16 (1999) 749-768 · LaTeX2e (IOP style), 24 pages, to be published in Class. Quantum Grav
arxiv created 1998/11/25 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We develop a Hamiltonian formulation of the Bianchi type I spacetime in conformal gravity - the theory described by the Lagrangian , which involves the quadratic curvature invariant constructed from the Weyl tensor, in a four-dimensional spacetime. We derive the explicit forms of the super-Hamiltonian and of the constraint expressing the conformal invariance of the theory and we write down the system of canonical equations. To seek out exact solutions of this system we add extra constraints on the canonical variables and we go through a global involution algorithm which eventually leads to the closure of the constraint algebra. The Painlevé approach provides us with a proof of non-integrability, as a consequence of the presence of movable logarithms in the general solution of the problem. We extract all possible particular solutions that may be written in closed analytical form. This enables us to demonstrate that the global involution algorithm has brought forth the complete list of exact solutions that may be written in closed analytical form. We discuss the conformal relationship, or absence thereof, of our solutions with Einstein spaces.