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arXiv · 1703.06024

General relativity with a positive cosmological constant $\lambda $ as a gauge theory

Marta Dudek·Janusz Garecki
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Abstract

In the paper we show that the general relativity action (and Lagrangian) in recent Einstein-Palatini formulation is equivalent to the action (and Langrangian) of a gauge field. We begin with a bit of information of the Einstein-Palatini (EP) action, then we present how Einstein fields equations can be derived from it. In the next section, we consider Einstein-Palatini action integral for general relativity with a positive cosmological constant $\Lambda $ in terms of $\hat{F}$, the curvature of the affine connection's pulled back from de Sitter bundle to Lorentz bundle. We will see that in terms of $\hat{F}$ this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the curvature $\hat{F}$.

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Marta Dudek, Janusz Garecki. 2017-03-17. General relativity with a positive cosmological constant $\lambda $ as a gauge theory. https://arxiv.org/abs/1703.06024

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