English

A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

General Relativity and Quantum Cosmology 2015-06-11 v2 High Energy Physics - Theory

Abstract

We consider a manifold endowed with two different vielbeins EAμE^{A}{}_{\mu} and LAμL^{A}{}_{\mu} corresponding to two different metrics gμνg_{\mu\nu} and fμνf_{\mu\nu}. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation gμνEAμLBν=gμνEBμLAνg^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu} can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.

Keywords

Cite

@article{arxiv.1208.4493,
  title  = {A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities},
  author = {Cedric Deffayet and Jihad Mourad and George Zahariade},
  journal= {arXiv preprint arXiv:1208.4493},
  year   = {2015}
}

Comments

20 pages. Section 7, prop. 6 and 7. added. Some results made more precise