A note on 'symmetric' vielbeins in bimetric, massive, perturbative and non perturbative gravities - INSPIRE

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

Aug, 2012

21 pages

Published in:

JHEP 03 (2013) 086

e-Print:

1208.4493 [gr-qc]

DOI:

10.1007/JHEP03(2013)086

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Abstract: (Springer)

We consider a manifold endowed with two different vielbeins and corresponding to two different metrics and f ( )μν( ). 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 can be imposed (or the “Deser-van Nieuwenhuizen” gauge chosen). We clarify and correct various statements which have been made about this issue. We show in particular that in D = 4 dimensions, this condition is always equivalent to the existence of a real matrix square root of f.

Note:

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

gravitation: massive
quantum gravity
perturbation theory
dimension: 2
dimension: 3
dimension: 4

References(27)

Figures(0)

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