Description of gravity in the model with independent nonsymmetric connection

Abstract

Abstract. A generalization of General Relativity is studied. The standard EinsteinHilbert 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.

Modifying the theory of gravity by changing independent variables

“…The main differences between this action and the standard one are that the Ricci tensor depends only on the connection and connection is an independent nonsymmetric variable. For the first time such action was considered by Einstein [5], but he also assumed that the metric is nonsymmetric too. It is easy to show that the theory with action (1) is completely equivalent to the GR.…”

“…It turns out that this theory can be interpreted as unified theory of gravity and electromagnetism, however, some additional assumptions were used by the authors to introduce a matter in the theory. A more natural way to add a classical matter in such theory was proposed in [4], [5].…”