Gravitational Dynamics of Cold Matter using the Deformation Tensor

Details Gravitational Dynamics of Cold Matter using the Deformation Tensor Gravitational Dynamics of Cold Matter using the Deformation Tensor

1996-09-23

arxiv.org/abs/astro-ph/9609156v1

Astron.Astrophys.315:11-20,1996

Astronomy and Astrophysics

Astrophysics

12 pages,l-aa.sty macro. latex with postscript figures. Accepted in A&A. Send Preprint request to edouard@gin.obspm.fr

Scientific paper

In this paper we present a new local Lagrangian approximation to the gravitational dynamics of cold matter. We describe the dynamics of a Lagrangian fluid element through only one quantity, the deformation tensor. We show that this tensor is clearly suited to the study of gravitational dynamics and, moreover, that knowing its evolution is enough to completely describe a fluid element. Our approximate dynamics treat exactly the conservation of mass, of the velocity divergence and of the shear and is exact in the case of planar, cylindrical and spherical collapses. It also reproduces very accurately the evolution of all dynamical quantities for a very wide class of initial conditions as illustrated by a detailed comparison with the homogeneous ellipsoid model. Beside, we highlight, for the first time, the important dynamical role played by the Newtonian counterpart of the magnetic part of the Weyl tensor.

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