Physics
Scientific paper
Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cqgra...4.1093s&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 4, Sept. 1, 1987, p. 1093-1117.
Physics
16
Einstein Equations, Ideal Fluids, Relativity, Space-Time Functions, Spherical Coordinates, Differential Equations, Fluid Flow, Shear Flow, Spherical Harmonics
Scientific paper
Two classes of methods for deriving an exact solution of the Einstein field equations representing shear-free motion of a spherically symmetric perfect fluid are discussed. The methods of McVittie (1984) and Nariai (1968) assume that a convenient class of metrics form one group, and the methods of Kustaanheimo and Qvist (1948), Chakravarty et al. (1976), and Wyman (1978) involve the suitable selection of an arbitrary function of integration. A generalization of the McVittie class of metrics is found to be trivial. It is noted that the assumption used by Nariai can be replaced by a weaker assumption to yield a solution. Following Wyman's procedure, a characteristic function is derived which yields all the explicitly known solutions.
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