A big-bang cylindrically symmetric radiation universe

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Abstract
A new nonstationary cylindrically symmetric solution to Einstein’s equations is given for a perfect fluid. The solution has a time singularity (t=0) at which the pressure p and density μ are equal to +∞ throughout the radial coordinate range 0≤r<∞, but for t>0 the model is well behaved. The fluid has the equation of state p= (1)/(3) μ, and for any fixed t>0 both p and μ are finite, decreasing monotonically to zero as r increases through the range 0≤r<∞. At any fixed r (0≤r<∞) both p and μ decrease steadily to zero as t increases through the range 0≤t<∞. The motion is irrotational, with shear, expansion and acceleration while the solution is algebraically general of Petrov type I.