scholarly journals On the classic geometrodynamics of a spherically-symmetric configuration of gravitational and electromagnetic fields

2019 ◽  
Vol 27 (1) ◽  
pp. 3-8
Author(s):  
V. D. Gladush

Analytical aspects of the classical geometrodynamics for the spherically-symmetric configuration of the electromagnetic and gravitational fields in GR are considered. The feature of such configurations is that they admit two motion integrals – the total mass and charge. The Einstein-Hilbert action for the configuration, after dimensional reduction, by means of the Legendre transformation is reduced to the Hamiltonian action. Using the conservation laws for the mass and charge, as well as the Hamiltonian constraint, the momenta are found as functions of configuration variables. The set of equations, which associate momenta and functional derivatives of the action in the configuration space (CS) is integrable. This allows us to obtain the action functional as a solution of the Einstein-Hamilton-Jacobi equation in functional derivatives. Variations of the action functional with respect to mass M and charge Q of the configuration lead to the motion trajectories in the CS. We note that the minisuperspace metric, which is induced by the kinetic part of the Lagrangian, does not coincide with the CS metric that arises when the function of lapse N is excluded from the action. The space-time metric for which the indicated metrics coincide in the T-region up to a coefficient are considered. The metric of CS is constructed and its geometry is studied. Under the trivial embedding of hypersurfaces of the foliation into a dynamical T-region, the CS is flat. It allows introducing pseudo-Cartesian coordinates in which the CS metric takes the Lorentz form.

2021 ◽  
Vol 34 ◽  
pp. 11-17
Author(s):  
V.D. Gladush

Some properties of the configuration space (CS) of charged black holes (BH) we are considered. A reduced action for the spherically symmetric configuration of the gravitational and electromagnetic fields is constructed. We restrict ourselves to considering of T-region, where the studied fields have a dynamic meaning. Using the Hamiltonian constraint, we exclude the nondynamic degree of freedom. This leads to the action of the system in the CS with the corresponding supermetric. It turns out that the CS is flat, and its metric admits a twoparametric group of motions. This group generates conservation laws for the geodesic equations. The first law is the charge conservation law, and second is the mass conservation law (the mass function). Using the Hamiltonian constraint, they allow one to find momenta as a function of the field variables andcalculate the action as a function of the conserved quantities and field variables in CS. We emphasize that to find this  action, we use only the integrability condition for a differential form. The quantization of the system is reduced to the  uantization of a free particle in a three-dimensional pseudo-Euclidean space. The natural measure corresponding to the CS metric is used to construct the Hermitian DeWitt and mass operators. Based on the self-consistent solution of quantum  DeWitt equations and equations for the eigenvalues of the mass and charge operators, the wave function for the spherically  symmetric configuration of the gravitational and electromagnetic fields in the T- region is constructed. As a result, we get a model of charged BH with continuous mass and charge spectra.


1976 ◽  
Vol 7 (44) ◽  
pp. no-no
Author(s):  
T. R. BORONOEVA ◽  
N. N. BELYAEV ◽  
M. D. STADNICHUK ◽  
A. A. PETROV

1965 ◽  
Vol 6 (1) ◽  
pp. 1-5 ◽  
Author(s):  
P. G. Bergmann ◽  
M. Cahen ◽  
A. B. Komar

1973 ◽  
Vol 9 (8) ◽  
pp. 951-952 ◽  
Author(s):  
V. I. Shvedov ◽  
V. K. Vasil'eva ◽  
O. B. Romanova ◽  
A. N. Grinev

1974 ◽  
Vol 51 (1) ◽  
pp. 43
Author(s):  
W. C. Fernelius ◽  
Kurt Loening ◽  
Roy M. Adams

1973 ◽  
Vol 9 (12) ◽  
pp. 1473-1475 ◽  
Author(s):  
V. I. Shvedov ◽  
V. K. Vasil'eva ◽  
Yu. I. Trofimkin ◽  
A. N. Grinev

2012 ◽  
Vol 27 (24) ◽  
pp. 1230023 ◽  
Author(s):  
TREVOR B. DAVIES ◽  
CHARLES H.-T. WANG ◽  
ROBERT BINGHAM ◽  
J. TITO MENDONÇA

We present a brief review on a new dynamical mechanism for a strong field effect in scalar–tensor theory. Starting with a summary of the essential features of the theory and subsequent work by several authors, we analytically investigate the parametric excitation of a scalar gravitational field in a spherically symmetric radially pulsating neutron star.


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