On Generating a Lagrangian for Higher Dimensional Gravity

TL;DR

This paper explores the mathematical foundation of the Lovelock Lagrangian in higher-dimensional gravity, linking it to Weil polynomials and the Weil homomorphism, thus providing a deeper geometric understanding.

Contribution

It establishes a connection between the Lovelock Lagrangian and Weil polynomials, offering a novel geometric perspective on higher-dimensional gravity theories.

Findings

Lovelock Lagrangian derived from Weil polynomials

Connection between Weil homomorphism and gravity Lagrangians

Provides a geometric interpretation of higher-dimensional gravity

Abstract

The Lovelock Lagrangian is for even dimension D obtained from Weil polynomials on the Lie algebra of the Lorentz group SO(1,D-1). The procedure for generating it is related to the Weil homomorphism that converts Lie algebra invariants into cohomology classes.