Space-timePub Date : 2019-05-28DOI: 10.1201/9781315165141-12
J. Allday
{"title":"Gravitational Waves","authors":"J. Allday","doi":"10.1201/9781315165141-12","DOIUrl":"https://doi.org/10.1201/9781315165141-12","url":null,"abstract":"(a) gμνA ν = (b) If ∂ν is the contravariant gradient operator, η ∂ν = (c) ggjk = (d) ggAγδ = (e) If n̂ is a unit vector, then nni = (f) In spatial coordinates, δ i = 2. Start with a metric of the form gμν = ημν +hμν . From the definition of the Christoffel symbols Γμν and the Riemann tensor R μ νρσ, show that to linear order in hμν , the Riemann tensor becomes Rμνρσ = 1 2 (∂ν∂ρhμσ + ∂μ∂σhνρ − ∂μ∂ρhνσ − ∂ν∂σhμρ) . (1)","PeriodicalId":179016,"journal":{"name":"Space-time","volume":"253 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132152917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Space-timePub Date : 2019-03-01DOI: 10.1201/9781315165141-4
Jonathan Allday
{"title":"The Theory of Special Relativity","authors":"Jonathan Allday","doi":"10.1201/9781315165141-4","DOIUrl":"https://doi.org/10.1201/9781315165141-4","url":null,"abstract":"Albert Einstein (1879-1955) published his first work on relativity in 1905, the same year in which he published remarkable papers on Brownian motion and the photoelectric effect. At the time he did this work, he was a patent examiner in the Swiss Patent Office. He was awarded the Nobel Prize for physics in 1921 \"for his services to the theory of physics, and especially for his discovery of the law of the photoelectric effect.\" He became a professor of physics at several German universities, and in 1916, he took a position at the Kaiser Wilhelm Institute in Berlin. As the Nazi party became powerful and finally took control of the country, Einstein became a target of the Nazi's anti-Jewish campaign. He left Germany with regret and found sanctuary in the United States. In 1933 he became a permanent staff member at the Institute for Advanced Studies at Princeton. He remained at that post for the rest of his life. Einstein proposed a solution to the puzzle posed by the Michelson-Morley results, and that work has come to be known as the theory of special relativity. Einstein's solution came as a surprise to most physicists because it was based not upon some strange new principle, but upon two postulates that would have been conceded by nearly all and upon a careful scrutiny of some accepted concepts. [excerpt]","PeriodicalId":179016,"journal":{"name":"Space-time","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123569463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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