Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame

Details Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame

Apr 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gregr..15..357l&link_type=abstract

General Relativity and Gravitation, Volume 15, Issue 4, pp.357-361

Physics

12

Scientific paper

All nonstatic spherically symmetric fluid solutions to the Einstein equations in the comoving frame ds^2 = e^{λ (r,t)} dr^2 + e^{μ (r,t)} dΩ ^2 - e^{v(r,t)} dt^2 are found subject to the conditions: (i)dot λ = Adot μ,A = const, (ii) λ,μ, andν are separable functions ofr andt, (iii) the heat flux vanishes, and (iv) the coefficient of shear viscosity vanishes. There are but two classes of solutions: (i)A= 1, in which case the metric reduces to the Robertson-Walker form, and (ii)A=0, in which case there are four solutions, all with nonvanishing acceleration, expansion, and shear. WithA=0, the solutions are either singular at the origin or degenerate into spaces of constant curvature.

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