scholarly journals ON THE STRUCTURE OF THE CONFIGURATION SPACE OF CHARGED BLACK HOLES

2021 ◽  
Vol 34 ◽  
pp. 11-17
Author(s):  
V.D. Gladush
Keyword(s):  
Black Holes ◽  
Electromagnetic Fields ◽  
Configuration Space ◽  
Conservation Law ◽  
Integrability Condition ◽  
Free Particle ◽  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Charged Black Holes ◽  
Symmetric Configuration

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.

scholarly journals Deformed General Relativity and Quantum Black Holes Interior

Universe ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 39 ◽  
Author(s):  
Denis Arruga ◽  
Jibril Ben Achour ◽  
Karim Noui
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Einstein Equations ◽  
Gravity Models ◽  
Effective Theory ◽  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Full Generality ◽  
Full Theory ◽  
Effective Theories

Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint, leading under some conditions to a notion of deformed covariance. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance cannot be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study static solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition. In particular, we give the expressions of the components of the effective metric (for spherically symmetric black holes interior) in terms of the functions that govern the deformations of the theory.

scholarly journals Dynamics of Electromagnetic Fields and Structure of Regular Rotating Electrically Charged Black Holes and Solitons in Nonlinear Electrodynamics Minimally Coupled to Gravity

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 205 ◽  
Author(s):  
Irina Dymnikova ◽  
Evgeny Galaktionov
Keyword(s):  
Black Holes ◽  
Electromagnetic Fields ◽  
Nonlinear Electrodynamics ◽  
Axially Symmetric ◽  
De Sitter ◽  
Dynamical Equations ◽  
Naked Singularities ◽  
Charged Black Holes ◽  
De Sitter Vacuum ◽  
Electrically Charged

We study the dynamics of electromagnetic fields of regular rotating electrically charged black holes and solitons replacing naked singularities in nonlinear electrodynamics minimally coupled to gravity (NED-GR). They are related by electromagnetic and gravitational interactions and described by the axially symmetric NED-GR solutions asymptotically Kerr-Newman for a distant observer. Geometry is described by the metrics of the Kerr-Schild class specified by T t t = T r r ( p r = − ρ ) in the co-rotating frame. All regular axially symmetric solutions obtained from spherical solutions with the Newman-Janis algorithm belong to this class. The basic generic feature of all regular objects of this class, both electrically charged and electrically neutral, is the existence of two kinds of de Sitter vacuum interiors. We analyze the regular solutions to dynamical equations for electromagnetic fields and show which kind of a regular interior is favored by electromagnetic dynamics for NED-GR objects.

Inflationary cosmological universe containing dark matter and many charged galaxies

1988 ◽  
Vol 66 (11) ◽  
pp. 1031-1034
Author(s):  
A Das ◽  
Daniel Kay
Keyword(s):  
Black Holes ◽  
Dark Matter ◽  
Time Evolution ◽  
Electromagnetic Fields ◽  
Cosmological Solution ◽  
Charged Matter ◽  
Charged Black Holes ◽  
The Third ◽  
Exact Cosmological Solution ◽  
The Universe

Within the framework of Einstein's theory, cosmological universes are considered that contain three types of "fluids." A neutral cosmological fluid (dark matter), which is present everywhere, determines the overall time evolution of the universe. The second type consists of charged matter that constitutes the cores of galaxies. The electromagnetic fields generated by the charged matter make up the third kind of fluid, which is evidently null. An exact cosmological solution is furnished that provides for an early inflationary period and contains many charged black holes as galactic cores.

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
Keyword(s):  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Action Functional ◽  
Hamiltonian Action ◽  
Gravitational Fields ◽  
Motion Trajectories ◽  
Symmetric Configuration ◽  
Functional Derivatives ◽  
Derivatives Of ◽  
Hamilton Jacobi Equation

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.

scholarly journals Spherically symmetric charged black holes with wavy scalar hair

2021 ◽  
Author(s):  
Yves Brihaye ◽  
Betti Hartmann
Keyword(s):  
Black Holes ◽  
Electromagnetic Coupling ◽  
Spherically Symmetric ◽  
Gravitational Coupling ◽  
The Novel ◽  
Maxwell Theory ◽  
Charged Black Holes ◽  
Scalar Hair ◽  
Complex Valued ◽  
Black Hole Solutions

Abstract We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating “wave packet” and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.

WIGGLY STRINGS OF RADIAL CONFIGURATION IN THE SCHWARZSCHILD AND REISSNER–NORDSTRÖM BLACK HOLES

2011 ◽  
Vol 26 (19) ◽  
pp. 3275-3285 ◽  
Author(s):  
HIROMI SUZUKI
Keyword(s):  
Black Holes ◽  
Equatorial Plane ◽  
Radial Direction ◽  
Spherically Symmetric ◽  
Classical Motion ◽  
Charged Black Holes ◽  
Open Strings

We study classical motion of a string in (3+1)-dimensional spherically symmetric neutral and charged black holes. The solutions for the wiggly string exhibit open strings lying in the radial direction in the equatorial plane outside the horizon.

Regular black holes and self-gravitating solitons with DE interiors

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040053 ◽  
Author(s):  
Irina Dymnikova
Keyword(s):  
Black Holes ◽  
Dark Matter ◽  
Dark Energy ◽  
Electromagnetic Fields ◽  
Naked Singularities ◽  
Charged Black Holes ◽  
Regular Black Holes ◽  
Electrically Charged ◽  
Rotating Objects

We outline the basic generic features of regular black holes and self-gravitating solitons replacing naked singularities with Dark Energy (DE) interiors, including thermodynamics of horizons and products of black holes evaporation as dark matter candidates with DE interiors, two kinds of interiors for rotating objects, electrically charged black holes and spinning solitons and non-dissipative source of their electromagnetic fields and geometry.

scholarly journals Spherically Symmetric Scalar Hair for Charged Black Holes

2020 ◽  
Vol 125 (11) ◽  
Author(s):  
Jeong-Pyong Hong ◽  
Motoo Suzuki ◽  
Masaki Yamada
Keyword(s):  
Black Holes ◽  
Spherically Symmetric ◽  
Charged Black Holes ◽  
Scalar Hair
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