of Lagrangian equations, and consider a restricted class of solutions when $\theta^0$, $\bar\theta_0$ are functions of $t$ only while $\theta^r$, $\bar\theta_r$ are functions of $r$. We shall show that even for this restricted class their role can be very different: For example, to obtain the Schwarzschild metric one should choose trivial solution for Lagrange multipliers and ghosts, otherwise the metric components will not have the Galilean form at infinity. On the contrary, in the case of the Lemaitre –- Tolman – Bondi model gauge-noninvariant sector of the model (gauge-fixing and ghost components) can imitate dust matter with zero pressure and energy density given by (\[dust.sol\]). In the end of this section we shall refer to our earlier papers where the role of gauge-noninvariant sector has been analyzed for systems with finite number degrees of freedom.

As it was done in Section 3.1, for simplicity we choose one of the gauge conditions in the form $N^r=0$ (\[g.c.2.1\]). Under this condition Eq. (\[eLbtr\]) reads $$\label{eLbtr_1}
\ddot\theta^r-\frac d{dt}\left(\frac{N^2}{V^2}(\theta^0)'\right)=0.$$ This equation is satisfied if $$\label{tsol}
\theta^0=\theta^0(t),\qquad
\theta^r=\theta^r(r).$$ Indeed, the condition (\[g.c.2.1\]) imposes limitations on possible coordinates transformations, so that the admissible transformations of $t$, $r$ are $\tau=\tau(t)$, $\rho=\rho(r)$. The infinitesimal parameters $\eta^0$, $\eta^r$ in 