# Einstein's static universe

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Application of the theory of relativity to the universe as a whole

**Einstein's static universe**, aka the **Einstein universe** or the **Einstein static eternal universe**, is a relativistic model of the universe proposed by [Albert Einstein](/source/Albert_Einstein) in 1917.[1][2] Shortly after completing the [general theory of relativity](/source/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](/source/Closed_universe) [spatial curvature](/source/Spatial_curvature).

To achieve a consistent solution to the [Einstein field equations](/source/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](/source/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/*R*2 = *κρ*/2, where *κ* is the [Einstein gravitational constant](/source/Einstein_gravitational_constant).[3]

Following the discovery by [Edwin Hubble](/source/Edwin_Hubble) of a linear relation between the [redshifts of the galaxies and their distance](/source/Redshift#Expansion_of_space) in 1929,[4] Einstein abandoned his static model of the universe and proposed expanding models such as the [Friedmann–Einstein universe](/source/Friedmann%E2%80%93Einstein_universe) and the [Einstein–de Sitter universe](/source/Einstein%E2%80%93de_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] In many Einstein biographies, it is claimed that Einstein referred to the cosmological constant in later years as his "biggest blunder". The astrophysicist [Mario Livio](/source/Mario_Livio) has recently cast doubt on this claim, suggesting that it may be exaggerated.[10]

## See also

- [Timeline of cosmological theories](/source/Timeline_of_cosmological_theories)

## References

1. **[^](#cite_ref-1)** Einstein, Albert (1917). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie" [Cosmological considerations on the general theory of relativity]. *Sitzungs. König. Preuss. Akad.* (in German): Sitzungsb. König. Preuss. Akad. 142–152.

1. **[^](#cite_ref-2)** Lorentz H.A.; Einstein A.; Minkowski H.; H. Weyl (1923). *The Principle of Relativity*. New York: Metheun & Co. pp. 175–188.

1. **[^](#cite_ref-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](/source/ArXiv_(identifier)):[1701.07261](https://arxiv.org/abs/1701.07261). [Bibcode](/source/Bibcode_(identifier)):[2017EPJH...42..431O](https://ui.adsabs.harvard.edu/abs/2017EPJH...42..431O). [doi](/source/Doi_(identifier)):[10.1140/epjh/e2017-80002-5](https://doi.org/10.1140%2Fepjh%2Fe2017-80002-5). [S2CID](/source/S2CID_(identifier)) [119461771](https://api.semanticscholar.org/CorpusID:119461771).

1. **[^](#cite_ref-4)** Hubble, Edwin (1929). ["A relation between distance and radial velocity among extra-galactic nebulae"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC522427). *Proceedings of the National Academy of Sciences*. **15** (3): 168–173. [Bibcode](/source/Bibcode_(identifier)):[1929PNAS...15..168H](https://ui.adsabs.harvard.edu/abs/1929PNAS...15..168H). [doi](/source/Doi_(identifier)):[10.1073/pnas.15.3.168](https://doi.org/10.1073%2Fpnas.15.3.168). [PMC](/source/PMC_(identifier)) [522427](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC522427). [PMID](/source/PMID_(identifier)) [16577160](https://pubmed.ncbi.nlm.nih.gov/16577160).

1. **[^](#cite_ref-5)** Einstein, Albert (1931). "Zum kosmologischen Problem der allgemeinen Relativitätstheorie". *Sitzungsb. König. Preuss. Akad.*: 235–237.

1. **[^](#cite_ref-6)** Einstein, Albert (1946). *Relativity: The Special and General Theories* (16th ed.). New York: Metheun. p. 137.

1. **[^](#cite_ref-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](/source/ArXiv_(identifier)):[1312.2192](https://arxiv.org/abs/1312.2192). [Bibcode](/source/Bibcode_(identifier)):[2014EPJH...39...63O](https://ui.adsabs.harvard.edu/abs/2014EPJH...39...63O). [doi](/source/Doi_(identifier)):[10.1140/epjh/e2013-40038-x](https://doi.org/10.1140%2Fepjh%2Fe2013-40038-x). [S2CID](/source/S2CID_(identifier)) [53419239](https://api.semanticscholar.org/CorpusID:53419239).

1. **[^](#cite_ref-8)** Nussbaumer and Bieri (2009). *Discovering the Expanding Universe*. Cambridge: Cambridge University Press. p. 147.

1. **[^](#cite_ref-9)** A. S. Eddington (9 May 1930). ["On the Instability of Einstein's Spherical World"](https://doi.org/10.1093%2Fmnras%2F90.7.668). *Monthly Notices of the Royal Astronomical Society*. **90** (7): 668–678. [doi](/source/Doi_(identifier)):[10.1093/mnras/90.7.668](https://doi.org/10.1093%2Fmnras%2F90.7.668).

1. **[^](#cite_ref-10)** [Zimmer, Carl](/source/Carl_Zimmer) (9 June 2013). ["The Genius of Getting It Wrong: *Brilliant Blunders* by Mario Livio"](https://web.archive.org/web/20130618190609/http://www.nytimes.com/2013/06/09/books/review/brilliant-blunders-by-mario-livio.html?pagewanted=all). *[The New York Times](/source/The_New_York_Times)*. Archived from [the original](https://www.nytimes.com/2013/06/09/books/review/brilliant-blunders-by-mario-livio.html) on 18 June 2013.

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