the gauge conditions (\[d.c.11\]), (\[d.c.22\]), while the equations (\[DPN\]), (\[DPNr\]) reproduce the constraints (\[eLN\]), (\[eLNr\]) in the Lagrangian formalism. The equations (\[DV\]) – (\[DPW\]) for physical gravitational degrees of freedom after some rearrangement can be shown to be equivalent to the dynamical Lagrangian equations (\[eLV\]), (\[eLW\]), and Eqs. (\[Dt0\]) – (\[DbPtr\]) are equivalent to the ghost equations (\[eLbt0\]) – (\[eLtr\]). Thus, in this Section we have got two sets of extended equations for our spherically symmetric model in the Lagrangian and Hamiltonian formalisms, which are proved to be completely equivalent. In the next Section we shall consider some particular solutions to these equations.

Particular solutions to the extended set of equations
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Solutions to gauge invariant Einstein equations.
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It is obvious enough that if we put all ghost as well as the Lagrange multipliers $\pi_N$, $\pi_{N^r}$ equal to zero in the extended set of equations (\[eLN\]) – (\[eLtr\]), we would return to gauge invariant Einstein equations for the model. The ghost equations (\[eLbt0\]) – (\[eLtr\]) are satisfied identically, so in this case we have just four equations (\[eLN\]) – (\[eLW\]) and two gauge conditions (\[d.c.11\]), (\[d.c.22\]). For further simplification of the equations we choose the condition (\[g.c.2\]) in the 