Valentin Gladush - Academia.edu (original) (raw)

Papers by Valentin Gladush

Research paper thumbnail of Classical and Quantum Descriptions of the Geometrodynamics of Black Holes

Deleted Journal, 2024

Analytical aspects of the classical and quantum geometrodynamics of charged black hole are consid... more Analytical aspects of the classical and quantum geometrodynamics of charged black hole are considered. We start with a reduced action for a spherically symmetric of Maxwell-Einstein system written in characteristic variables. The feature of these configurations is that they admit two motion integrals, the total mass and charge. Momenta and constraint are introduced. Using the conservation laws and the Hamiltonian constraint, the momenta as functions of configuration variables are found. It turns out that the system of equations relating momenta and functional derivatives of an action on a 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 and charge of the configuration lead to the motion trajectories in the CS. Further, the space-temporal action is transformed into an action in the configuration space similar to the Jacobi action of classical mechanics. This induces a metric in the CS. Thus, the metric on the CS is introduced and its geometry is studied. The field variables transformation is obtained which brings the CS metric to the "quasi-Lorentzian" form. On this basis, quantization is considered. Taking into account the structure of the CS, the momentum operators, DeWitt equations, mass and charge operators are constructed. Further, for comparison, consider the reduced CBH model defined in the T-region. In this simplified formulation, the T-model equations are integrated and lead to CBH with a continuous spectrum of mass and charge.

Research paper thumbnail of Spherically Symmetric System of Gravitational and Electromagnetic Fields and the Structure of Its Configuration Space

Odessa Astronomical Publications

Geometrodynamics of charged black holes (BH) described by the system of Maxwell Einstein equation... more Geometrodynamics of charged black holes (BH) described by the system of Maxwell Einstein equations is considered. We start from a spherically symmetric metric, a reduced action, and a Lagrangian written in characteristic variables. The configuration space (CS) metric, Hamiltonian, momentum and electromagnetic constraints are constructed. The system has conservation laws of charge q and mass m. The action functional is transformed into a Jacobi-type functional in CS with a metric conformal to the CS metric. A transformation of field variables is introduced which brings the CS metric to the "Lorentzian"form. The resulting CS metric is the metric of a flat nonholonomic section of a 4-dimensional space. In the new variables, the squared momenta of the system has the Lorentz form. On this basis, quantization is considered. Thanks to the structure of the CS, the momentum operators, the DeWitt equations, and the mass and charge operators are constructed. The equations system of C...

Research paper thumbnail of T-Solutions of the 5D Kaluza-Klein Model

Odessa Astronomical Publications, 2019

Research paper thumbnail of On the quantum model of a charged black hole

Journal of Physics and Electronics

We study the quantum states of the black hole model in the configuration space. To this end, we i... more We study the quantum states of the black hole model in the configuration space. To this end, we investigate the properties of the configuration space of the Einstein–Maxwell set of equations in the T-region. We limit ourselves to considering the T-region, where the fields under consideration have a dynamic meaning. Based on the standard action for the of Einstein–Maxwell set of equations, we construct the reduced action for the spherical symmetry case. Using the Hamiltonian constraint, we exclude the non-dynamic degree of freedom from the reduced action, thereby passing to the configuration space. In the new representation of the system, we study the induced dynamical system in the configuration space. It turns out that the induced supermetric is reduced to a quasi-Cartesian form. The laws of charge and mass conservation, which the system contains, together with the Hamilton constraint, completely determine thestate of the black hole. They allow one to find the momenta and the actio...

Research paper thumbnail of Quantum Spectrum on the Naked Reissner-Nordstrom Background

Odessa Astronomical Publications, 2013

The eigen frequencies of a massless scalar field in the space-time of the Reissner-Nordstrom sing... more The eigen frequencies of a massless scalar field in the space-time of the Reissner-Nordstrom singularity are studied by using the WKB approxima­tion and by numerical integration of the wave equation. Both these approaches indicate the existence of long living states for the singularity charge-to-mass ratios being close enough to the extremal value Q/M = 1.

Research paper thumbnail of Motion Types of Neutral Test Particles in the Field of Charged Object in General Relativity and Their Classification

Odessa Astronomical Publications, 2013

In the previous work of one of the au­thors the radial motions of charged test particles in the f... more In the previous work of one of the au­thors the radial motions of charged test particles in the field of a spherically symmetric charged object in gen­eral relativity were considered and their classification was built. The present paper generalizes this approach to study the motion of particles with non-zero orbital momentum. We limit the consideration to neutral par­ticles and stress on the peculiarities that emerge in the case of the Reissner-Nordstrom field with super­extremal charge.

Research paper thumbnail of On the effective actions for the spherical charged dust shell in General Relativity

A simple and direct, based on the equations of motion, derivation of the variational principle an... more A simple and direct, based on the equations of motion, derivation of the variational principle and effective actions for a spherical charged dust shell in general relativity is offered. This principle is based on the relativistic version of the DÆAlembert principle of virtual displacements and leads to the effective actions for the shell, which describe the shell from the point of view of the exterior or interior stationary observers. Herewith, sides of the shell are considered independently, in the coordinates of the interior or exterior region of the shell. Canonical variables for a charged dust shell are built. It is shown that the conditions of isometry of the sides of the shell lead to the Hamiltonian constraint on these interior and exterior dynamical systems. Special cases of the ôhollowö and ôscreeningö shells are briefly considered, as well as a family of the concentric charged dust shells.

Research paper thumbnail of The generalized Casimir operator and tensor representations of groups

There has been proposed a new method of the constructing of the basic functions for spaces of ten... more There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the Lie derivatives instead of the corresponding infenitisemal operators. When introducing the generalized Casimir operator we use the metric for which a group being considered will be isometry that follows from the invariance condition for the generalized Casimir operator. This allows us to formulate the eigenvalue and eigenfunction problems correctly. The invariant projection operators have been constructed in order to separate irreducible components. The cases of the Bianchi type G^3 IX and G^3 II groups are considered as examples.

Research paper thumbnail of The quasi-classical model of the spherical configuration in general relativity

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gra... more We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in General Relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-class...

Research paper thumbnail of Stable and decaying bound states on the naked Reissner-Nordström background

We present a quantum mechanical study of the bound states of a neutral scalar particle on the cur... more We present a quantum mechanical study of the bound states of a neutral scalar particle on the curved background described by the Reissner-Nordström (RN) spacetime that corresponds to a naked singularity. We show that there occurs both the metastable, i.e. decaying bound states and the stable ones. The corresponding energy spectra are calculated in the leading WKB approximation and the comparison with the RN black hole quasinormal mode spectrum is made. The metastable bound states on the naked singularity background turn out to be more long-living than the quasinormal modes for the black hole with the same mass.

Research paper thumbnail of On the Stable Spherically-Symmetric Charged Dust Configurations in General Relativity

The radial motion of a self-graviting charged dust and stability condition of the static charged ... more The radial motion of a self-graviting charged dust and stability condition of the static charged dust spheres are considered. The stability is possible for the bound states of the weakly charged layer with abnormal charge with respect to the active mass.

Research paper thumbnail of Toward the Quantization of Black Holes

Odessa Astronomical Publications, 2016

In order to construct a quantum model of black hole (BH), we introduce a modified description of ... more In order to construct a quantum model of black hole (BH), we introduce a modified description of classical space-time BH (the Schwarzschild solution). We develop the Lagrangian formalism of the vacuum gravitational field in spherically symmetric space-time, divided on the two regions: R-and Tregions. Initial metrics in their regions are taken in the scale-invariant form and depend on a timelike coordinate in T-region and space-like coordinate in R-region. We introduce the Hamiltonian and mass function, which corresponding evolutional coordinate (t or r) in each of regions. Their Poisson brackets are proportional Hamiltonian constraint. Further we construct the quantum operators of Hamilton and masse. Their commutator are proportional to the Hamilton operator. System of Wheeler-De Witt equation and equation on the own values of mass operator, together with the compatibility condition, allow to find wave functions in every region. These wave functions form the common wave function of BH with the continuous masse spectrum.

Research paper thumbnail of On the Structure of the Configuration Space of Charged Black Holes

Background: Students with sickle cell disease are at risk for poor academic performance due to th... more Background: Students with sickle cell disease are at risk for poor academic performance due to the combined and/or interactive effects of environmental, psychosocial, and disease-specific factors. Poor academic performance has significant social and health consequences. Objective: To study academic achievement and attainment in children with sickle cell disease in the United States. Design: Medline, Embase, SCOPUS, CINAHL, ERIC, and PsycINFO were searched for peer-reviewed articles. Studies of children (ages 5-18) diagnosed with sickle cell disease of any genotype reporting academic achievement (standardized tests of reading, math, and spelling) or attainment (grade retention or special education) outcomes were included. Outcomes were analyzed using a random effects model. Achievement scores were compared to within study controls or normative expectations. Prevalence of grade retention and special education services were compared to national (United States) estimates for Black students. Age at assessment and overall IQ were evaluated separately for association with reading and mathematics scores. Subgroup analyses of reading and math scores were analyzed by cerebral infarct status (no cerebrovascular accident, silent infarct, stroke). Results: There were 44 eligible studies. Students with sickle cell disease scored 0.70, 0.87, and 0.80 (p < 0.001) SD below normative expectations on measures of reading, mathematics, and spelling, respectively. Compared to unaffected sibling and/or healthy controls (k = 8, n = 508), reading and math scores were 0.40 (p = 0.017) and 0.36 (p = 0.033) SD below expectations. Grade retention was approximately 10 times higher in students with sickle cell disease than Black students nationally. Intellectual functioning explained 97.3 and 85.8% of the variance in reading and mathematics performance, respectively (p < 0.001). Subgroup analyses revealed significant differences in reading (p = 0.034) and mathematics (p < 0.001) based on infarct status, with lower performance associated with presence of a silent infarct or stroke. Heitzer et al. Academic Performance Sickle Cell Disease Conclusion: Students with sickle cell disease demonstrate notable academic difficulties and are at high risk for grade retainment. Development of academic interventions and increased access to school support services are needed for this vulnerable population.

Research paper thumbnail of Five-dimensional general relativity and Kaluza-Klein theory

We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations a... more We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations are constructed and 5D analog of the mass function is found. The corresponding conservation law leads to 5D analog of Birkhoff’s theorem. Hence the cylinder condition is dynamically implemented for the considered spaces. For some obtained metrics a period of space with respect to the fifth coordinate was found. The problem of the dynamical degrees of freedom of the fields system obtained in the process of dimensional reduction is discussed, and the problem of their interpretation is considered. One can think that the parametrization of the scalar field and 4D metric leading to the conformally invariant 4D theory for interacting gravitational and scalar fields is most natural and adequate. 1

Research paper thumbnail of Five Dimensional Boosts and Electromagnetic Field in Kaluza-Klein Theory

A stationary, spherically symmetric, 5D Kaluza-Klein theory exhibits 5D boosts. After reduction o... more A stationary, spherically symmetric, 5D Kaluza-Klein theory exhibits 5D boosts. After reduction of 5D vacuum Einstein action of a diagonal 5D metric, we obtained Einstein equations with energy-momentum tensor of a massless scalar field. Applying a 5D boost generates a non-diagonal metric with an electric field. This electric field is trivial, since it can be removed by a reverse 5D boost. Existence of such kind of trivial fields is analyzed on the example previously known solutions. Transformation properties of physical fields relative to 5D boosts examined. This symmetry is a subgroup of SL(3, R) symmetries of 5D equations, rewritten in 3+ 2-decomposition in stationary, spherically symmetric case. This symmetry also can be used to generate new solutions. The solution with trivial electric field is obtained from diagonal 5D metric by a simple symmetry transformation, which reduces to the coordinate 5D boosts.

Research paper thumbnail of The Model for Final Stage of Gravitational Collapse Massless Scalar Field

Odessa Astronomical Publications, Jun 10, 2015

Research paper thumbnail of Quantum Model of a Charged Black Hole

Odessa Astronomical Publications, Nov 7, 2017

Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions... more Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψ em with a dened total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the conguration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result. Keywords: charged black holes, mass and charge functions, constraints, mass and charge operators, the compatibility condition.

Research paper thumbnail of On the variational principle for dust shells in General Relativity

The variational principle for a thin dust shell in General Relativity is constructed. The princip... more The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to “natural boundary conditions” on the shell. These conditions and the gravitational field equations which follow from an initial variational principle, are used for elimination of the gravitational degrees of freedom. The transformation of the variational formula for spherically-symmetric systems leads to two natural variants of the effective action. One of these variants describes the shell from a stationary interior observer’s point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints. The canonical equivalence of the mentioned systems is shown in the extended phase space. Some particular cases are considered.

Research paper thumbnail of Classification for the radial component of particles motion in the field of a super-extremely charged object

arXiv: General Relativity and Quantum Cosmology, 2011

A method for investigation of neutral test particles motion with the angular momentum L in the Re... more A method for investigation of neutral test particles motion with the angular momentum L in the Reissner-Nordstr\"om field of a super-extremely charged object with mass M and charge Q > M is proposed. The problem of classifying the radial component of motion is reduced to working up a classification for "effective" potential types and subsequent consideration of trajectories for each of these types.

Research paper thumbnail of The model of dark galactic halo based on equilibrium distribution function

arXiv: General Relativity and Quantum Cosmology, 2011

The model of galactic halo as a system of the collisionless small neutral particles from the stan... more The model of galactic halo as a system of the collisionless small neutral particles from the standpoint of kinetic theory is considered. For the equilibrium system with the use of Maxwell-Boltzmann distribution we obtained results which explain the observed flat rotation curve. These results practically coincide with the results of equilibrium spherical gas cloud model in Newtonian gravitation with linear state equation.

Research paper thumbnail of Classical and Quantum Descriptions of the Geometrodynamics of Black Holes

Deleted Journal, 2024

Analytical aspects of the classical and quantum geometrodynamics of charged black hole are consid... more Analytical aspects of the classical and quantum geometrodynamics of charged black hole are considered. We start with a reduced action for a spherically symmetric of Maxwell-Einstein system written in characteristic variables. The feature of these configurations is that they admit two motion integrals, the total mass and charge. Momenta and constraint are introduced. Using the conservation laws and the Hamiltonian constraint, the momenta as functions of configuration variables are found. It turns out that the system of equations relating momenta and functional derivatives of an action on a 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 and charge of the configuration lead to the motion trajectories in the CS. Further, the space-temporal action is transformed into an action in the configuration space similar to the Jacobi action of classical mechanics. This induces a metric in the CS. Thus, the metric on the CS is introduced and its geometry is studied. The field variables transformation is obtained which brings the CS metric to the "quasi-Lorentzian" form. On this basis, quantization is considered. Taking into account the structure of the CS, the momentum operators, DeWitt equations, mass and charge operators are constructed. Further, for comparison, consider the reduced CBH model defined in the T-region. In this simplified formulation, the T-model equations are integrated and lead to CBH with a continuous spectrum of mass and charge.

Research paper thumbnail of Spherically Symmetric System of Gravitational and Electromagnetic Fields and the Structure of Its Configuration Space

Odessa Astronomical Publications

Geometrodynamics of charged black holes (BH) described by the system of Maxwell Einstein equation... more Geometrodynamics of charged black holes (BH) described by the system of Maxwell Einstein equations is considered. We start from a spherically symmetric metric, a reduced action, and a Lagrangian written in characteristic variables. The configuration space (CS) metric, Hamiltonian, momentum and electromagnetic constraints are constructed. The system has conservation laws of charge q and mass m. The action functional is transformed into a Jacobi-type functional in CS with a metric conformal to the CS metric. A transformation of field variables is introduced which brings the CS metric to the "Lorentzian"form. The resulting CS metric is the metric of a flat nonholonomic section of a 4-dimensional space. In the new variables, the squared momenta of the system has the Lorentz form. On this basis, quantization is considered. Thanks to the structure of the CS, the momentum operators, the DeWitt equations, and the mass and charge operators are constructed. The equations system of C...

Research paper thumbnail of T-Solutions of the 5D Kaluza-Klein Model

Odessa Astronomical Publications, 2019

Research paper thumbnail of On the quantum model of a charged black hole

Journal of Physics and Electronics

We study the quantum states of the black hole model in the configuration space. To this end, we i... more We study the quantum states of the black hole model in the configuration space. To this end, we investigate the properties of the configuration space of the Einstein–Maxwell set of equations in the T-region. We limit ourselves to considering the T-region, where the fields under consideration have a dynamic meaning. Based on the standard action for the of Einstein–Maxwell set of equations, we construct the reduced action for the spherical symmetry case. Using the Hamiltonian constraint, we exclude the non-dynamic degree of freedom from the reduced action, thereby passing to the configuration space. In the new representation of the system, we study the induced dynamical system in the configuration space. It turns out that the induced supermetric is reduced to a quasi-Cartesian form. The laws of charge and mass conservation, which the system contains, together with the Hamilton constraint, completely determine thestate of the black hole. They allow one to find the momenta and the actio...

Research paper thumbnail of Quantum Spectrum on the Naked Reissner-Nordstrom Background

Odessa Astronomical Publications, 2013

The eigen frequencies of a massless scalar field in the space-time of the Reissner-Nordstrom sing... more The eigen frequencies of a massless scalar field in the space-time of the Reissner-Nordstrom singularity are studied by using the WKB approxima­tion and by numerical integration of the wave equation. Both these approaches indicate the existence of long living states for the singularity charge-to-mass ratios being close enough to the extremal value Q/M = 1.

Research paper thumbnail of Motion Types of Neutral Test Particles in the Field of Charged Object in General Relativity and Their Classification

Odessa Astronomical Publications, 2013

In the previous work of one of the au­thors the radial motions of charged test particles in the f... more In the previous work of one of the au­thors the radial motions of charged test particles in the field of a spherically symmetric charged object in gen­eral relativity were considered and their classification was built. The present paper generalizes this approach to study the motion of particles with non-zero orbital momentum. We limit the consideration to neutral par­ticles and stress on the peculiarities that emerge in the case of the Reissner-Nordstrom field with super­extremal charge.

Research paper thumbnail of On the effective actions for the spherical charged dust shell in General Relativity

A simple and direct, based on the equations of motion, derivation of the variational principle an... more A simple and direct, based on the equations of motion, derivation of the variational principle and effective actions for a spherical charged dust shell in general relativity is offered. This principle is based on the relativistic version of the DÆAlembert principle of virtual displacements and leads to the effective actions for the shell, which describe the shell from the point of view of the exterior or interior stationary observers. Herewith, sides of the shell are considered independently, in the coordinates of the interior or exterior region of the shell. Canonical variables for a charged dust shell are built. It is shown that the conditions of isometry of the sides of the shell lead to the Hamiltonian constraint on these interior and exterior dynamical systems. Special cases of the ôhollowö and ôscreeningö shells are briefly considered, as well as a family of the concentric charged dust shells.

Research paper thumbnail of The generalized Casimir operator and tensor representations of groups

There has been proposed a new method of the constructing of the basic functions for spaces of ten... more There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the Lie derivatives instead of the corresponding infenitisemal operators. When introducing the generalized Casimir operator we use the metric for which a group being considered will be isometry that follows from the invariance condition for the generalized Casimir operator. This allows us to formulate the eigenvalue and eigenfunction problems correctly. The invariant projection operators have been constructed in order to separate irreducible components. The cases of the Bianchi type G^3 IX and G^3 II groups are considered as examples.

Research paper thumbnail of The quasi-classical model of the spherical configuration in general relativity

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gra... more We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in General Relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-class...

Research paper thumbnail of Stable and decaying bound states on the naked Reissner-Nordström background

We present a quantum mechanical study of the bound states of a neutral scalar particle on the cur... more We present a quantum mechanical study of the bound states of a neutral scalar particle on the curved background described by the Reissner-Nordström (RN) spacetime that corresponds to a naked singularity. We show that there occurs both the metastable, i.e. decaying bound states and the stable ones. The corresponding energy spectra are calculated in the leading WKB approximation and the comparison with the RN black hole quasinormal mode spectrum is made. The metastable bound states on the naked singularity background turn out to be more long-living than the quasinormal modes for the black hole with the same mass.

Research paper thumbnail of On the Stable Spherically-Symmetric Charged Dust Configurations in General Relativity

The radial motion of a self-graviting charged dust and stability condition of the static charged ... more The radial motion of a self-graviting charged dust and stability condition of the static charged dust spheres are considered. The stability is possible for the bound states of the weakly charged layer with abnormal charge with respect to the active mass.

Research paper thumbnail of Toward the Quantization of Black Holes

Odessa Astronomical Publications, 2016

In order to construct a quantum model of black hole (BH), we introduce a modified description of ... more In order to construct a quantum model of black hole (BH), we introduce a modified description of classical space-time BH (the Schwarzschild solution). We develop the Lagrangian formalism of the vacuum gravitational field in spherically symmetric space-time, divided on the two regions: R-and Tregions. Initial metrics in their regions are taken in the scale-invariant form and depend on a timelike coordinate in T-region and space-like coordinate in R-region. We introduce the Hamiltonian and mass function, which corresponding evolutional coordinate (t or r) in each of regions. Their Poisson brackets are proportional Hamiltonian constraint. Further we construct the quantum operators of Hamilton and masse. Their commutator are proportional to the Hamilton operator. System of Wheeler-De Witt equation and equation on the own values of mass operator, together with the compatibility condition, allow to find wave functions in every region. These wave functions form the common wave function of BH with the continuous masse spectrum.

Research paper thumbnail of On the Structure of the Configuration Space of Charged Black Holes

Background: Students with sickle cell disease are at risk for poor academic performance due to th... more Background: Students with sickle cell disease are at risk for poor academic performance due to the combined and/or interactive effects of environmental, psychosocial, and disease-specific factors. Poor academic performance has significant social and health consequences. Objective: To study academic achievement and attainment in children with sickle cell disease in the United States. Design: Medline, Embase, SCOPUS, CINAHL, ERIC, and PsycINFO were searched for peer-reviewed articles. Studies of children (ages 5-18) diagnosed with sickle cell disease of any genotype reporting academic achievement (standardized tests of reading, math, and spelling) or attainment (grade retention or special education) outcomes were included. Outcomes were analyzed using a random effects model. Achievement scores were compared to within study controls or normative expectations. Prevalence of grade retention and special education services were compared to national (United States) estimates for Black students. Age at assessment and overall IQ were evaluated separately for association with reading and mathematics scores. Subgroup analyses of reading and math scores were analyzed by cerebral infarct status (no cerebrovascular accident, silent infarct, stroke). Results: There were 44 eligible studies. Students with sickle cell disease scored 0.70, 0.87, and 0.80 (p < 0.001) SD below normative expectations on measures of reading, mathematics, and spelling, respectively. Compared to unaffected sibling and/or healthy controls (k = 8, n = 508), reading and math scores were 0.40 (p = 0.017) and 0.36 (p = 0.033) SD below expectations. Grade retention was approximately 10 times higher in students with sickle cell disease than Black students nationally. Intellectual functioning explained 97.3 and 85.8% of the variance in reading and mathematics performance, respectively (p < 0.001). Subgroup analyses revealed significant differences in reading (p = 0.034) and mathematics (p < 0.001) based on infarct status, with lower performance associated with presence of a silent infarct or stroke. Heitzer et al. Academic Performance Sickle Cell Disease Conclusion: Students with sickle cell disease demonstrate notable academic difficulties and are at high risk for grade retainment. Development of academic interventions and increased access to school support services are needed for this vulnerable population.

Research paper thumbnail of Five-dimensional general relativity and Kaluza-Klein theory

We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations a... more We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations are constructed and 5D analog of the mass function is found. The corresponding conservation law leads to 5D analog of Birkhoff’s theorem. Hence the cylinder condition is dynamically implemented for the considered spaces. For some obtained metrics a period of space with respect to the fifth coordinate was found. The problem of the dynamical degrees of freedom of the fields system obtained in the process of dimensional reduction is discussed, and the problem of their interpretation is considered. One can think that the parametrization of the scalar field and 4D metric leading to the conformally invariant 4D theory for interacting gravitational and scalar fields is most natural and adequate. 1

Research paper thumbnail of Five Dimensional Boosts and Electromagnetic Field in Kaluza-Klein Theory

A stationary, spherically symmetric, 5D Kaluza-Klein theory exhibits 5D boosts. After reduction o... more A stationary, spherically symmetric, 5D Kaluza-Klein theory exhibits 5D boosts. After reduction of 5D vacuum Einstein action of a diagonal 5D metric, we obtained Einstein equations with energy-momentum tensor of a massless scalar field. Applying a 5D boost generates a non-diagonal metric with an electric field. This electric field is trivial, since it can be removed by a reverse 5D boost. Existence of such kind of trivial fields is analyzed on the example previously known solutions. Transformation properties of physical fields relative to 5D boosts examined. This symmetry is a subgroup of SL(3, R) symmetries of 5D equations, rewritten in 3+ 2-decomposition in stationary, spherically symmetric case. This symmetry also can be used to generate new solutions. The solution with trivial electric field is obtained from diagonal 5D metric by a simple symmetry transformation, which reduces to the coordinate 5D boosts.

Research paper thumbnail of The Model for Final Stage of Gravitational Collapse Massless Scalar Field

Odessa Astronomical Publications, Jun 10, 2015

Research paper thumbnail of Quantum Model of a Charged Black Hole

Odessa Astronomical Publications, Nov 7, 2017

Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions... more Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψ em with a dened total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the conguration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result. Keywords: charged black holes, mass and charge functions, constraints, mass and charge operators, the compatibility condition.

Research paper thumbnail of On the variational principle for dust shells in General Relativity

The variational principle for a thin dust shell in General Relativity is constructed. The princip... more The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to “natural boundary conditions” on the shell. These conditions and the gravitational field equations which follow from an initial variational principle, are used for elimination of the gravitational degrees of freedom. The transformation of the variational formula for spherically-symmetric systems leads to two natural variants of the effective action. One of these variants describes the shell from a stationary interior observer’s point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints. The canonical equivalence of the mentioned systems is shown in the extended phase space. Some particular cases are considered.

Research paper thumbnail of Classification for the radial component of particles motion in the field of a super-extremely charged object

arXiv: General Relativity and Quantum Cosmology, 2011

A method for investigation of neutral test particles motion with the angular momentum L in the Re... more A method for investigation of neutral test particles motion with the angular momentum L in the Reissner-Nordstr\"om field of a super-extremely charged object with mass M and charge Q > M is proposed. The problem of classifying the radial component of motion is reduced to working up a classification for "effective" potential types and subsequent consideration of trajectories for each of these types.

Research paper thumbnail of The model of dark galactic halo based on equilibrium distribution function

arXiv: General Relativity and Quantum Cosmology, 2011

The model of galactic halo as a system of the collisionless small neutral particles from the stan... more The model of galactic halo as a system of the collisionless small neutral particles from the standpoint of kinetic theory is considered. For the equilibrium system with the use of Maxwell-Boltzmann distribution we obtained results which explain the observed flat rotation curve. These results practically coincide with the results of equilibrium spherical gas cloud model in Newtonian gravitation with linear state equation.