Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-10-02
Class.Quant.Grav. 18 (2001) 4897-4920
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, 11 figures, accepted for publication in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/18/22/313
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.
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