Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...423...22c&link_type=abstract
The Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 423, no. 1, p. 22-32
Astronomy and Astrophysics
Astrophysics
45
Cosmic Dust, Cosmology, Galactic Clusters, Gravitational Effects, Perturbation Theory, Relativistic Particles, Dark Matter, Eigenvalues, Hamilton-Jacobi Equation, Red Shift, Taylor Series
Scientific paper
Starting from general relativity, we give a systematic derivation of the Zel'dovich approximation describing the nonlinear evolution of collisionless dust. We begin by evolving dust along world lines, and we demonstrate that the Szekeres line element is an exact but apparently unstable solution of the evolution equations describing pancake collapse. Next, we solve the Einstein field equations by employing Hamilton-Jacobi techniques and a spatial gradient expansion. We give a prescription for evolving a primordial or 'seed' metric up to the formation of pancakes, and demonstrate its validity by rederiving the Szekeres solution approximately at third order and exactly at fifth order in spatial gradients. Finally we show that the range of validity of the expansion can be improved quite significantly if one notes that the 3-metric must have nonnegative eigenvalues. With this improvement the exact Szekeres solution is obtained after only one iteration.
Croudace K. M.
Parry Joe
Salopek David S.
Stewart John M.
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