Description of gravity in the model with independent nonsymmetric connection

TL;DR

This paper explores a generalized gravity model using a nonsymmetric connection in the Palatini formalism, revealing how electromagnetic potential can emerge from space-time geometry through independent connection dynamics.

Contribution

It introduces a generalized gravity framework with an independent nonsymmetric connection, deriving electromagnetic phenomena from geometric properties of space-time.

Findings

Electromagnetic potential arises from the geometry of space-time.

The model reproduces Einstein, geodesic, and Maxwell equations.

Connection gauge invariance leads to arbitrary connection determination.

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.