const}=\frac{C_3}2.$$ and non-zero components of $T_{\mu(obs)}^{\nu}$ are $$\label{obs00_2}
T^0_{0(obs)}=T^1_{1(obs)}=\frac1{8\pi}\frac{C_3}{W^2}.$$ Then instead of (\[Schw.sol\]) we get $$\label{Schw.sol.1}
V(r)=\frac1{\sqrt{1+C_3-\displaystyle\frac{2GM}r}}.$$ The requirement for metric components to have the Galilean form at infinity means that $C_3=0$ and all components of $T_{\mu(obs)}^{\nu}$ are zero.

### The Lemaitre –- Tolman – Bondi solution.

This solution is rather interesting. From (\[eLbt0\_2\]), (\[eLt0r\_2\]) and (\[Tobs\]) we obtain $$\label{pi-theta}
\dot{\bar\theta_0}={\rm const};\qquad
\dot{\theta_0}={\rm const};\qquad
\dot\pi_N=\varphi(r),$$ and, after the substitution of (\[LTB.sol\]), for non-zero components of $T_{\mu(obs)}^{\nu}$, $T_{\mu(ghost)}^{\nu}$ we have $$\label{obs00_3}
T^0_{0(obs)}=\frac1{4\pi}\frac{\varphi_1(r)}{W'W^2};\qquad
T^0_{0(ghost)}=\frac1{4\pi}\frac{\varphi_2(r)}{W'W^2},$$ $\varphi(r)$, $\varphi_1(r)$, $\varphi_2(r)$ are arbitrary functions. We can see that the both quasi-tensors $T_{\mu(ghost)}^{\nu}$, $T_{\mu(obs)}^{\nu}$ describe a medium with zero pressure and energy density of the form (\[dust.sol\]). The meaningful feature of this consideration is that we do not need to introduce an extra dust matter into the model, while a dust matter is simulated by its ghost and gauge-fixing components.

### Models with finite numbers of degrees of freedom.

In our early papers ([@SSV2] and others) it was demonstrated for models with finite numbers of degrees of freedom that the quasi-tensor $T_{\mu(obs)}^{\nu}$ describes a continual medium with the equation of state essentially depending on the parametrization of the gauge variable and the gauge condition for it. It 