A General Expression for the Quartic Lovelock Tensor

TL;DR

This paper derives a comprehensive formula for the quartic Lovelock tensor in n-dimensional manifolds, expressing it through fundamental curvature tensors, and provides related coefficients for the Lovelock Lagrangian and lower-order tensors.

Contribution

It presents a general expression for the quartic Lovelock tensor in terms of basic curvature tensors, extending the mathematical framework of Lovelock gravity.

Findings

Provides explicit formulas for the quartic Lovelock tensor.

Includes coefficients for the Lovelock Lagrangian and lower-order tensors.

Enhances understanding of curvature invariants in higher-dimensional gravity theories.

Abstract

A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In addition, expressions are given (in the appendix) for the coefficient of the quartic Lovelock Lagrangian as well as for lower-order Lovelock tensors and Lovelock Lagrangian coefficients.