1924
DOI: 10.2307/2298148
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The Mathematical Theory of Relativity.

Abstract: 20. The mathematical notion of a vector 21. The physical notion of a vector 22. The summation convention 23. Tensors 24. Inner multiplication and contraction. 25. The fundamental tensors . 26. Associated tensors 27. Christoffel's 3-index symbols 28. Equations of a geodesic 29. Covariant derivative of a vector 30. Covariant derivative of a tensor 31. Alternative discussion of the covariant derivative 32. Surface-elements and Stokes's theorem 33. Significance of covariant differentiation 34.

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Cited by 11 publications
(15 citation statements)
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“…The idea of generalizing the Einstein-Hilbert action by including higher-order terms can be traced back to the early years of general relativity (see, e.g., [29]). Nevertheless, only in the last decades these models have attracted more attention, and the main motivation for this comes from the quantum theory.…”
Section: Higher-derivative Gravity Modelsmentioning
confidence: 99%
“…The idea of generalizing the Einstein-Hilbert action by including higher-order terms can be traced back to the early years of general relativity (see, e.g., [29]). Nevertheless, only in the last decades these models have attracted more attention, and the main motivation for this comes from the quantum theory.…”
Section: Higher-derivative Gravity Modelsmentioning
confidence: 99%
“…Therefore, Lemaitre knew remarkable observations of redshifts done by V. Slipher [10] 4 and he clearly understood that it was very important to find observational features of a proposed model and really the velocity -distance could be such a test for a proposed cosmological model. Moreover, A. Eddington discussed radial velocities of spiral galaxies observed by V. Slipher as an important criterium to test a cosmological model [19] (he considered the de Sitter model in in his book).…”
Section: Early Cosmological Studiesmentioning
confidence: 99%
“…Therefore, it is crucial to comprehend the inherent geometry of spacetime and the procedure for embedding a 4D space-time. In line with this, Karmarkar [58] has embedded 4-dimensional spacetime into 5-dimensional Euclidean space. This embedding simplifies the process of solving the Einstein field equations.…”
Section: Introductionmentioning
confidence: 88%
“…Further, to be a Class I static and non-static spherically symmetric spacetime, it must satisfy the following Karmarkar condition [58]…”
Section: B the Class I Condition For The Decoupled Systemmentioning
confidence: 99%
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