An exact Lagrangian integral for the Newtonian gravitational field strength
arXiv:gr-qc/0508059 · doi:10.1016/j.physleta.2006.01.045
Abstract
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.
arXiv comment15 pages, section on applications added; matches published version in Phys.Lett.A
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- Nonstandard approach to gravity for the dark sector of the Universe
- Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)