Classical analysis of Bianchi types I and II in Ashtekar variables

1994/12/06 by G. González, Gabriela Gonzalez, Ranjeet S. Tate +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Classical mechanics #Mathematical physics #Nonlinear Waves and Solitons #Physics #Quantum chaos and dynamical systems #gr-qc

paper · pdf · doi:10.1088/0264-9381/12/5/018

published as Class.Quant.Grav.12:1287-1304,1995 · Latex, uses revtex, 13 pages in 10pt

arxiv created 1994/12/06 · openalex publication_date 1995/05/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We solve the complex Einstein equations for Bianchi I and II models formulated in Ashtekar variables. We then solve the reality conditions to obtain a parametrization of the space of Lorentzian solutions in terms of real canonically conjugate variables. In the Ashtekar variables, the dynamics of the universe point particle is governed by only a curved supermetric---there is no potential term. In the usual metric formulation the particle bounces off a potential wall in flat superspace. We consider possible characterizations of this `bounce' in the potential-free Ashtekar variables.

Citations

• Empty Space-Times Admitting a Three Parameter Group of Motions
• New Variables for Classical and Quantum Gravity
• Oscillatory approach to the singular point in relativistic cosmology
• Geometrical Theorems on Einstein's Cosmological Equations