CLASSICAL DESCRIPTIONS OF THE GEOMETRODYNAMICS OF CHARGED BLACK HOLES
Analytical aspects of the classical geometrodynamics of charged black holes are considered. The classical model of the charged BHs is the spherically symmetric configuration of the electromagnetic and gravitational fields in GR. The feature of such dynamic systems is that, in addition to the Killing vector, they admit two motion integrals: the total mass M and the charge Q of the con?guration. Using
these conservation laws, as well as the Hamiltonian constraint, the momenta as functions of configuration variables are found. In addition, the integrability
conditions for the momenta as functional derivatives of the action are satisfied. This allows us to calculate the functional of action, which is a solution of the
Einstein-Hamilton-Jacobi equation. Variations of action functional with respect to the mass M and charge Q lead to the solution of the Einstein equations
in the con?guration space.
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