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6.6 Tensor perturbations

The covariant description of tensor modes on the brane is via the shear, which satisfies the wave equation [219]
[ ( )] 2 ¨ 1- 2 r- 2( E E ) \~/ smn - smn - 5Hsmn - 2/\ + 2k r - 3p - (r + 3p)c smn - k pmn + 2Hp mn . (332)
Unlike the density and vector perturbations, there is no closed system on the brane for large scales. The KK anisotropic stress pEmn is an unavoidable source for tensor modes on the brane. Thus it is necessary to use the 5D metric-based formalism. This is the subject of the next Section 7.

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