The Zeldovich approximation and the relativistic Hamilton-Jacobi equation
Feb, 199425 pages
Published in:
- Mon.Not.Roy.Astron.Soc. 271 (1994) 1005
e-Print:
- astro-ph/9403053 [astro-ph]
Report number:
- DAMTP-R-94-6,
- ALBERTA-THY-06-94
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Abstract: (arXiv)
Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity potential. It is shown that the velocity of the field may always be derived from a potential which however may be a multi-valued function of the space-time coordinates. In the Newtonian limit, the results are nonlocal because one must solve the Newton-Poisson equation. By considering the Hamilton-Jacobi equation for general relativity, we set up gauge-invariant equations which respect causality. A spatial gradient expansion leads to simple and useful results which are local --- they require only derivatives of the initial gravitational potential.Note:
- 25 pages, DAMTP R94/6, ALBERTA THY/06-94
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