Kaluza-Klein Formalism of General Spacetimes

TL;DR

This paper introduces a Kaluza-Klein formalism for general 4-dimensional spacetimes using a (2,2)-fibration approach, decomposing the metric into tensor, gauge, and scalar fields, with applications discussed.

Contribution

It presents a novel Kaluza-Klein framework for general relativity based on (2,2)-fibration, enabling new insights into metric decomposition and gauge structures.

Findings

Metric coefficients decompose into tensor, gauge, and scalar fields.

The formalism reveals transformation properties under diffeomorphisms.

Applications demonstrate the utility of the approach in general relativity.

Abstract

I describe the Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-fibration of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. It is shown that the metric coefficients can be decomposed into sets of fields, which transform as a tensor field, gauge fields, and scalar fields with respect to the infinite dimensional group of the diffeomorphisms of the 2-dimensional fibre space. I discuss a few applications of this formalism.