Generalized Metrical Multi-Time Lagrange Geometry of Physical Field

TL;DR

This paper develops a geometric framework on jet bundles to model gravitational and electromagnetic fields, deriving Einstein and Maxwell equations within a unified metrical multi-time Lagrange geometry setting.

Contribution

It introduces a generalized metrical multi-time Lagrange geometric model for physical fields, extending classical theories to a broader mathematical context.

Findings

Provides a geometric model for gravitational and electromagnetic fields.

Derives Einstein and Maxwell equations in the new framework.

Unifies field theories within a generalized jet bundle geometry.

Abstract

The paper developes a geometrization of a Kronecker $h$-regular vertical fundamental metrical d-tensor $G^{(\alpha)(\beta)}_{(i)(j)}$ on the jet fibre bundle of order one $J^1(T,M)$. This geometrization gives a mathematical model for both gravitational and electromagnetic field theory, in a general setting. In this context, the Einstein and Maxwell equations are described.