CLASSICAL DESCRIPTIONS OF THE GEOMETRODYNAMICS OF CHARGED BLACK HOLES

Abstract

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.

Keywords

• electromagnetic and gravitational fields
• geometrodynamics
• constraints
• , configuration space
• einstein-hamilton-jacobi equation