Abstract
Hoyle1 has shown that for a steady-state universe consisting of uniformly distributed matter of density ρ a metric of the form: 
applies if it is assumed that a uniform creation of matter occurs.
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References
Hoyle, F., Mon. Not. Roy. Astro. Soc., 108, 372 (1948).
Hawkins, G. S., Astro. J., 65, 52 (1960).
Stephenson, L. M., J. Inst. Elec. Eng., 10, 312 (1964).
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STEPHENSON, L. Cosmological Red-shift. Nature 204, 1180 (1964). https://doi.org/10.1038/2041180a0
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DOI: https://doi.org/10.1038/2041180a0
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