2005/08/31 by Thomas Buchert · 1 citation
Mathematics · Physics and Astronomy · #astro-ph #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1016/j.physleta.2006.01.045
published as Phys.Lett. A354 (2006) 8-14 · 15 pages, section on applications added; matches published version in Phys.Lett.A
arxiv created 2006/01/23 · arxiv updated 2009/12/01
An exact expression for the gravitational field strength in a self-gravitating dust continuum is derived within the Lagrangian picture of continuum mechanics. From the Euler-Newton system a transport equation for the gravitational field strength is formulated and then integrated along trajectories of continuum elements. The resulting integral solves one of the Lagrangian equations of the corresponding Lagrange-Newton system in general. Relations to known exact solutions without symmetry in Newtonian gravity are discussed. The presented integral may be employed to access the non-perturbative regime of structure formation in Newtonian cosmology, and to apply iterative Lagrangian schemes to solve the Lagrange-Newton system.