Eur. Phys. J. C (2008) 53: 99-108
https://doi.org/10.1140/epjc/s10052-007-0441-1

Regular Article - Theoretical Physics

Gauge formulation for higher order gravity

¹ Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, CEP 01405-900, São Paulo, SP, Brazil
² Universidade Vale do Rio Verde de Três Coracões, Av. Castelo Branco, 82 – Chácara das Rosas, P.O. Box 3050, CEP 37410-000, Três Coracões, MG, Brazil
³ Instituto de Fomento e Coordenacão Industrial, Comando-Geral de Tecnologia Aeroespacial, Praca Mal. Eduardo Gomes 50, CEP 12228-901, São José dos Campos, SP, Brazil

^* e-mail: cassius.anderson@gmail.com

Received: 30 July 2007
Revised: 28 August 2007
Published online: 1 November 2007

Abstract

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=∂F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky’s term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.