Einstein's static universe

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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.[1][2] 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.

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 gravitational constant.[3]

Following the discovery by Edwin Hubble of a linear relation between the redshifts of the galaxies and their distance in 1929,[4] 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".[5][6][7][8][9] And he considered as his biggest blunder.


  1. ^ Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie". Sitzungs. König. Preuss. Akad.: Sitzungsb. König. Preuss. Akad. 142–152.
  2. ^ Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). The Principle of Relativity. New York: Metheun & Co. pp. 175–188.
  3. ^ 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. Bibcode:2017EPJH...42..431O. doi:10.1140/epjh/e2017-80002-5.
  4. ^ Hubble, Edwin (1929). "A relation between distance and radial velocity among extra-galactic nebulae". Proceedings of the National Academy of Sciences. 15 (3): 168–173. Bibcode:1929PNAS...15..168H. doi:10.1073/pnas.15.3.168. PMC 522427. PMID 16577160.
  5. ^ Einstein, Albert (1931). "Zum kosmologischen Problem der allgemeinen Relativitätstheorie". Sitzungsb. König. Preuss. Akad.: 235–237.
  6. ^ Einstein, Albert (1946). Relativity: The Special and General Theories (16th ed.). New York: Metheun. p. 137.
  7. ^ 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. Bibcode:2014EPJH...39...63O. doi:10.1140/epjh/e2013-40038-x.
  8. ^ Nussbaumer and Bieri (2009). Discovering the Expanding Universe. Cambridge: Cambridge University Press. p. 147.
  9. ^ A. S. Eddington (9 May 1930). "On the Instability of Einstein's Spherical World". Monthly Notices of the Royal Astronomical Society. 90 (7): 668–678. doi:10.1093/mnras/90.7.668.