Teleparallel equivalent of higher dimensional gravity theories

TL;DR

This paper explores the teleparallel formulation of higher-dimensional gravity theories, establishing their equivalence with Lanczos-Lovelock gravity and analyzing their invariance properties and topological aspects.

Contribution

It demonstrates that the teleparallel equivalent of Lovelock gravity can be derived via dimensional continuation of teleparallel Euler characteristics, revealing new topological invariants.

Findings

Teleparallel equivalent of Lovelock gravity is obtained through dimensional continuation.

The teleparallel Euler characteristic is a closed, gauge-invariant form.

Lovelock actions are invariant under Poincare and diffeomorphism groups.

Abstract

The equivalence between the Lanczos-Lovelock and teleparallel gravities is discused. It is shown that the teleparallel equivalent of the Lovelock gravity action is generated by dimensional continuation of the teleparallel equivalent of the Euler characteristics associated to all the lower even dimensions. It is also found that the teleparallel equivalent of the (i) d-dimensional Euler characteristic is a closed form and gauge invariant, (ii) Lovelock action are invariant both under the Poincare group and diffeomorphisms.