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Axioms 2019, 8(1), 24; https://doi.org/10.3390/axioms8010024

General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory

1
Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
2
Institute of Mathematics and Cosmology Group, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
*
Author to whom correspondence should be addressed.
Received: 16 October 2018 / Revised: 30 January 2019 / Accepted: 4 February 2019 / Published: 21 February 2019
(This article belongs to the Special Issue Applications of Differential Geometry)
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PDF [250 KB, uploaded 4 March 2019]

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 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. View Full-Text
Keywords: action integral; fiber bundle; connection in a principal fiber bundle and its curvature; pull-back of forms; Lie groups and their algebras action integral; fiber bundle; connection in a principal fiber bundle and its curvature; pull-back of forms; Lie groups and their algebras
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Dudek, M.; Garecki, J. General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory. Axioms 2019, 8, 24.

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