An exact Lagrangian integral for the Newtonian gravitational field strength

Details An exact Lagrangian integral for the Newtonian gravitational field strength An exact Lagrangian integral for the Newtonian gravitational field strength

2005-08-15

arxiv.org/abs/gr-qc/0508059v3

Phys.Lett. A354 (2006) 8-14

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, section on applications added; matches published version in Phys.Lett.A

Scientific paper

10.1016/j.physleta.2006.01.045

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.

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