Characterization of the Lovelock gravity by Bianchi derivative

TL;DR

This paper establishes a new characterization of Lovelock gravity by demonstrating that its equations of motion can be derived from the trace of the Bianchi derivative of a specific curvature polynomial tensor.

Contribution

It proves that each term in the Lovelock Lagrangian corresponds to a divergence-free tensor derived from the Bianchi derivative, providing a novel geometric characterization.

Findings

Lovelock gravity tensors are linked to Bianchi derivatives.

The theorem applies to all polynomial curvature terms in Lovelock gravity.

Provides a geometric foundation for Lovelock gravity equations.

Abstract

We prove the theorem: The second order quasi-linear differential operator as a second rank divergence free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth rank tensor, which is a homogeneous polynomial in curvatures. The existence of such a tensor for each term in the polynomial Lagrangian is a new characterization of the Lovelock gravity.