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arXiv · 1803.05958

Description of gravity in the model with independent nonsymmetric connection

N. V. Kharuk·S. A. Paston·A. A. Sheykin
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Abstract

A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result of variation with respect to the metric Einstein equations are obtained. A variation with respect to the connection leads to an arbitrariness in the determination of connection, i.e. the presence of gauge invariance. Then a matter in a form of point particle which interacts with field of connection is introduced. Also the action is complemented by a kinetic term for field of the connection to avoid incompatible equation of motion. Thus after the variation procedures we obtain the Einstein equations, the geodesic equation and the Maxwell`s equations for electromagnetism, where some components of the connection play the role of the electromagnetic potential. Thereby the electromagnetic potential is obtained from the geometry of space-time.

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N. V. Kharuk, S. A. Paston, A. A. Sheykin. 2018-03-15. Description of gravity in the model with independent nonsymmetric connection. https://doi.org/10.1051/epjconf%2F201715805011

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