Boundary terms in Lovelock gravity from dimensionally continued Chern-Simons forms

TL;DR

This paper derives boundary terms for Lovelock gravity using the index theorem for manifolds with boundaries, providing a new geometric approach to understanding boundary contributions in higher curvature gravity theories.

Contribution

It introduces a novel method to obtain boundary terms in Lovelock gravity via the index theorem, extending the geometric understanding of boundary contributions.

Findings

Derived explicit boundary terms for Lovelock gravity

Connected boundary terms to the index theorem in differential geometry

Provided a geometric framework for boundary contributions in higher curvature theories

Abstract

Boundary terms for Lovelock gravity are obtained by calculating in arbitrary dimension the index theorem for the de Rham complex of a manifold with nonempty boundary.