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We construct Hamiltonian dynamics of the generalized spherically symmetricgravitational model in extended phase space. We start from the Faddeev - Popoveffective action with gauge-fixing and ghost terms, making use of gaugeconditions in differential form. It enables us to introduce missing velocitiesinto the Lagrangian and then construct a Hamiltonian function according a usualrule which is applied for systems without constraints. The main feature ofHamiltonian dynamics in extended phase space is that it can be proved to becompletely equivalent to Lagrangian dynamics derived from the effective action.We find a BRST invariant form of the effective action by adding terms notaffecting Lagrangian equations. After all, we construct the BRST chargeaccording to the Noether theorem. Our algorithm differs from that by Batalin,Fradkin and Vilkovisky, but the resulting BRST charge generates correcttransformations for all gravitational degrees of freedom including gauge ones.Generalized spherically symmetric model imitates the full gravitational theorymuch better then models with finite number of degrees of freedom, so that onecan expect appropriate results in the case of the full theory.

Generalized spherically symmetric gravitational model: Hamiltonian dynamics in extended phase space and BRST charge