Higher dimensional gravity invariant under the Poincare group

TL;DR

This paper demonstrates a formalism for constructing higher-dimensional gravity actions invariant under local Poincaré transformations, matching previously known coefficients, applicable in both even and odd dimensions.

Contribution

It introduces the Stelle-West Grignani-Nardelli formalism for higher-dimensional gravity invariant under Poincaré symmetry, extending previous results to all dimensions.

Findings

Constructed gravity actions invariant under local Lorentz and Poincaré groups.

Actions have coefficients identical to those in prior established models.

Applicable to both even and odd dimensional spacetimes.

Abstract

It is shown that the Stelle-West Grignani-Nardelli-formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincar\`{e} translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli in ref. Class. Quantum Grav. 17 (2000) 4451.