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

All nonstatic spherically symmetric fluid solutions to the Einstein equations in the comoving frame $$ds^2 = e^{\lambda (r,t)} dr^2 + e^{\mu (r,t)} d\Omega ^2 - e^{v(r,t)} dt^2$$ 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.