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Keywords = connection in a principal fiber bundle and its curvature

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9 pages, 250 KB  
Article
General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory
by Marta Dudek and Janusz Garecki
Axioms 2019, 8(1), 24; https://doi.org/10.3390/axioms8010024 - 21 Feb 2019
Cited by 1 | Viewed by 3403
Abstract
In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how [...] Read more.
In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r. We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r. Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
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