Einstein's static universe
{{Short description|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 in 1917.{{cite journal |last=Einstein |first=Albert |title=Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie |lang=de |trans-title=Cosmological considerations on the general theory of relativity |journal=Sitzungs. König. Preuss. Akad. |date=1917 |pages=Sitzungsb. König. Preuss. Akad. 142–152}}{{cite book|author1=Lorentz H.A. |author2=Einstein A. |author3=Minkowski H. |author4=H. Weyl |title=The Principle of Relativity|publisher=Metheun & Co.|location=New York|date = 1923|pages=175–188}}
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.{{cite journal|last1=O'Raifeartaigh |display-authors=etal |title=Einstein's 1917 static model of the universe: a centennial review|journal=Eur. Phys. J. H|date=2017|volume=42|issue=3|pages=431–474|doi=10.1140/epjh/e2017-80002-5|arxiv=1701.07261|bibcode=2017EPJH...42..431O|s2cid=119461771 }}
Following the discovery by Edwin Hubble of a linear relation between the redshifts of the galaxies and their distance in 1929,{{cite journal|last1=Hubble|first1=Edwin|title=A relation between distance and radial velocity among extra-galactic nebulae|journal=Proceedings of the National Academy of Sciences|date=1929|volume=15|issue=3|pages=168–173|doi=10.1073/pnas.15.3.168|pmid=16577160|pmc=522427|bibcode=1929PNAS...15..168H|doi-access=free}} 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".{{cite journal|last1=Einstein|first1=Albert|title=Zum kosmologischen Problem der allgemeinen Relativitätstheorie|journal=Sitzungsb. König. Preuss. Akad.|date = 1931|pages=235–237}}{{cite book|last1=Einstein|first1=Albert|title=Relativity: The Special and General Theories|date=1946|publisher=Metheun|location=New York|page=137|edition=16th}}{{cite journal|last1=O'Raifeartaigh and McCann|title=Einstein's cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe|journal=Eur. Phys. J. H|date=2014|volume=39|issue=1|pages=63–85|doi=10.1140/epjh/e2013-40038-x|arxiv=1312.2192|bibcode=2014EPJH...39...63O|s2cid=53419239}}{{cite book|last1=Nussbaumer and Bieri|title=Discovering the Expanding Universe|date=2009|publisher=Cambridge University Press|location=Cambridge|pages=147}}{{cite journal|author=A. S. Eddington |title=On the Instability of Einstein's Spherical World |journal=Monthly Notices of the Royal Astronomical Society |volume=90 |issue=7 |date=9 May 1930 |pages=668–678 |doi=10.1093/mnras/90.7.668 |doi-access=free}} 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 has recently cast doubt on this claim, suggesting that it may be exaggerated.{{Cite news |url=https://www.nytimes.com/2013/06/09/books/review/brilliant-blunders-by-mario-livio.html |url-access=subscription |archive-url=https://web.archive.org/web/20130618190609/http://www.nytimes.com/2013/06/09/books/review/brilliant-blunders-by-mario-livio.html?pagewanted=all |archive-date=18 June 2013 |title=The Genius of Getting It Wrong: Brilliant Blunders by Mario Livio |date=9 June 2013 |newspaper=The New York Times |last=Zimmer |first1=Carl |author-link=Carl Zimmer}}{{cbignore}}