Article

# Ghosts in Massive Gravity

(Impact Factor: 6.22). 05/2005; 0509. DOI: 10.1088/1126-6708/2005/09/003
Source: arXiv

ABSTRACT In the context of Lorentz-invariant massive gravity we show that classical solutions around heavy sources are plagued by ghost instabilities. The ghost shows up in the effective field theory at huge distances from the source, much bigger than the Vainshtein radius. Its presence is independent of the choice of the non-linear terms added to the Fierz-Pauli Lagrangian. At the Vainshtein radius the mass of the ghost is of order of the inverse radius, so that the theory cannot be trusted inside this region, not even at the classical level. Comment: 16 pages

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• "In fact, in first order form a qualitatively new problem can arise. In massive gravity, the standard problem is the Boulware–Deser (BD) ghost [38], see also [39] [40]. "
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ABSTRACT: We reconsider the possibility of a class of new kinetic terms in the first order (vielbein) formulation of massive gravity and multi-gravity. We find that new degrees of freedom emerge which are not associated with the Boulware--Deser ghost and are intrinsic to the vielbein formulation. These new degrees of freedom are associated with the Lorentz transformations which encode the additional variables contained in the vielbein over the metric. Although they are not guaranteed to be ghostly, they are nevertheless infinitely strongly coupled on Minkowski spacetime and are not part of the spin-2 multiplet. Hence their existence implies the uniqueness of the Einstein--Hilbert term as the kinetic term for a massive graviton.
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• "Under the scalar field redefinition [36] [37] χ = c m 2 φ, "
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• "As [5] discusses, in its page 92, that this easy recovery of the Schwartzshield metric, if a graviton mass goes to zero, is impossible. Also note that note [4] has a discussion on how the bending of light is not commensurate with GR for massive graviton, which is equivalent to a discussion on a phenomenological ghost state for the trace of ℎ, which is given by [6] and occurs regardless of whether the mass for graviton nearly goes to zero. In [7], Csáki et al., have given a temporary fix to restore the bending of light for massive gravitons and to remove the 3/4th angle deflection from the 1919 GR test value, and this is by the use of brane theory. "
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