there is a relation $$n'n\c{T}^{00}-a'a \eta_{ab}\c{T}^{ab}=-\m 
(\c{T}_{\b{0}\b{0}}-\eta_{ab}\c{T}_{\b{a}\b{b}})=-\m \c{T}_{\b{4}\b{4}}
.$$ Solving (\[g15\]), we have ł[g17]{} ()\^5 = {- (e\^[y]{} -1)} It is remarkable that the constants $B$ and $B'$ which appear in different equations are close to each other. The small difference between the constants can be attributed to approximations to the exact equations.

 Einstein equations with the bulk energy-momentum tensor
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Having the expressions for the bulk energy-momentum tensor $\c{T}^{ij}$, we are in position to find the range of $t$ and $y$ within which solutions of the Einstein equations with the bulk energy-momentum tensor included are sufficiently close to the leading-order solutions, i.e. can be considered as perturbations. In particular, in Sect.4 we determined the spectrum of Kaluza-Klein tower of gravitons in the leading approximation which is possible, if $\r/\m \ll 1$ and if corrections to the leading approximation are small.

Let us consider the $({}^0_0)$ component of the Einstein equations in the bulk ł[00]{} +- =2\^2 + Ţ\^0\_0 (y,t) The ratio of the bulk term to $2\m^2$ is ł[f8]{} = -= ()\^5 (y)e\^[5 y]{} where ł[f5]{} =()\^2()\^2 K()\^2 . Here we have used (\[2ca\]) to write $$\k^2 T^4 =\f{180 \r}{g_* (T) \pi^2},$$ where $g_* = g_s +g_v +7 g_f 