Statistics – Computation
Scientific paper
Sep 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990apj...360..315h&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 360, Sept. 10, 1990, p. 315-329.
Statistics
Computation
12
Cosmology, Einstein Equations, Relativity, Universe, Astronomical Models, Computational Astrophysics, Riemann Manifold, Schwarzschild Metric, Space-Time Functions
Scientific paper
Three alternative forms are presented for the Robertson-Walker line element of the k = -1 Riemannian curvature isotropic cosmological models, as well as two alternative forms for the k = 0 model and one form for the k = +1 model; these forms are directly derived by solving Einstein's field equations. It is then noted that McVittie's (1933) embedding of a Schwarzschild field in the Robertson-Walker spacetimes fits naturally into one each of the alternative line elements. Related solutions of Einstein's equations are derived with a perfect fluid source which fit naturally in the remaining two forms of the k = -1 universe and the one remaining form of the k = 0 universe. Three additional perfect fluid solutions of Einstein's equations that are in a different sense analogous to McVittie's original solutions are also presented.
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