Einstein's static universe
Einstein's static universe, also known as the Einstein universe or the Einstein world, is a relativistic model of the universe proposed by Albert Einstein in 1917. Shortly after completing the general theory of relativity, Einstein applied his new theory of gravity to the universe as a whole. Assuming a universe that was static in time, and possessed of a uniform distribution of matter on the largest scales, Einstein was led to a finite, static universe of spherical spatial curvature.
In order to achieve a consistent solution to the Einstein field equations for the case of a static universe with a non-zero density of matter, Einstein found it necessary to introduce a new term to the field equations, the cosmological constant. In the resulting model, the radius R and density of matter ρ of the universe were related to the cosmological constant λ according to λ = 1/R2 = κρ/2 where κ is the Einstein constant.
Following the discovery by Edwin Hubble of a linear relation between the redshifts of the galaxies and their distance in 1929, Einstein abandoned his static model of the universe and proposed expanding models such as the Friedmann-Einstein universe and the Einstein-de Sitter universe. In both cases, he set the cosmological constant to zero, declaring it "no longer necessary ... and theoretically unsatisfactory".
- Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". Sitzungs. König. Preuss. Akad.: Sitzungsb. König. Preuss. Akad. 142–152.
- Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). The Principle of Relativity. New York: Metheun & Co. pp. 175–188.
- O'Raifeartaigh et.al (2017). "Einstein's 1917 static model of the universe: a centennial review". Eur. Phys. J. H. 42 (3): 431–474. arXiv:1701.07261. doi:10.1140/epjh/e2017-80002-5.
- Hubble, Edwin (1929). "A relation between distance and radial velocity among extra-galactic nebulae". Proceedings of the National Academy of Sciences. 15: 168–173. doi:10.1073/pnas.15.3.168. PMC 522427. PMID 16577160.
- Einstein, Albert (1931). "Zum kosmologischen Problem der allgemeinen Relativitätstheorie". Sitzungsb. König. Preuss. Akad.: 235–237.
- Einstein, Albert (1946). Relativity: The Special and General Theories (16th ed.). New York: Metheun. p. 137.
- O'Raifeartaigh and McCann (2014). "Einstein's cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe". Eur. Phys. J. H. 39 (1): 63–85. arXiv:1312.2192. doi:10.1140/epjh/e2013-40038-x.
- Nussbaumer and Bieri (2009). Discovering the Expanding Universe. Cambridge: Cambridge University Press. p. 147.