Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame |
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Authors: | Kayll Lake |
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Affiliation: | 1. Department of Physics, Queen's University at Kingston, K7L 3N6, Kingston, Ontario, Canada
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Abstract: | All nonstatic spherically symmetric fluid solutions to the Einstein equations in the comoving frame $$ds^2 = e^{lambda (r,t)} dr^2 + e^{mu (r,t)} dOmega ^2 - e^{v(r,t)} dt^2$$ are found subject to the conditions: (i) (dot lambda = {rm A}dot mu) ,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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