Fibre bundle generated theory of higher dimensional gravity

TL;DR

This paper develops a new theoretical framework for higher-dimensional gravity using fibre bundle formalism and Weil polynomials, extending geometric methods to include Riemann-Cartan spacetimes.

Contribution

It introduces a fibre bundle-based Lagrangian formulation of higher-dimensional gravity leveraging Weil polynomials on the Poincaré Lie algebra.

Findings

Constructed a Lagrangian form for higher-dimensional gravity

Utilized Weil polynomials on the Poincaré Lie algebra

Applied the formalism to Riemann-Cartan spacetimes

Abstract

With the help of Weil polynomials on the Lie algebra of the Poincar\'e group in D dimensions, we construct a Lagrangian form for higher dimensional gravity on a principal fibre bundle whose base space is an even-dimensional Riemann-Cartan spacetime and whose structure group is the Poincar\'e group.