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No Ghost State in the Brane World
We discuss the role of the trace part of metric fluctuations in the
Randall-Sundrum scenario of gravity. Without the matter, this field
() is a gauge-dependent term, and thus it can be gauged
away. But, including the uniform source , this field satisfies
the linearized equation . This may
correspond to the scalar in the bending of the brane due to the
localized source. Considering the case of longitudinal perturbations (), one finds the source relation
, which leads to the ghost states in the
massive modes. In addition, if one requires , it is
found that in the limit of we have the massless spin-2
propagation without the ghost state. This exactly corresponds to the same
situation as in the intermediate scales of Gregory-Rubakov-Sibiryakov (GRS)
model.Comment: 7 pages, no figure, the version to appear in PLB, comments on the
matter source and references added, main results unchange
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