The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. A...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.展开更多
The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not prov...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not provide the complete set of equations for solids and, in contrast to the Newton gravitation theory, does not allow us to study the stresses induced by gravitation in solids, because the compatibility equations which are attracted in the Euclidean space for this purpose do not exist in the Riemannian space. To solve the problem within the framework of GR, a special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space in GR allows us to supplement the conservation equations for the energy-momentum tensor with compatibility equations of the theory of elasticity and to arrive to the complete set of equations for stresses. The analytical solution of the Einstein equations for the empty space surrounding the sphere and the numerical solution for the internal space inside the sphere with the proposed geometry are presented and discussed.展开更多
In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre ...In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.展开更多
We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We ...We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.展开更多
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not provide the complete set of equations for solids and, in contrast to the Newton gravitation theory, does not allow us to study the stresses induced by gravitation in solids, because the compatibility equations which are attracted in the Euclidean space for this purpose do not exist in the Riemannian space. To solve the problem within the framework of GR, a special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space in GR allows us to supplement the conservation equations for the energy-momentum tensor with compatibility equations of the theory of elasticity and to arrive to the complete set of equations for stresses. The analytical solution of the Einstein equations for the empty space surrounding the sphere and the numerical solution for the internal space inside the sphere with the proposed geometry are presented and discussed.
文摘In this paper, the axisymmetric problems of arbitrary thick spherical shell and solid sphere are studied directly from equilibrium equations of three-dimensional problem, and the general solutions informs of Legendre serifs for thick spherical shell and solid sphere are given by using the method of weighted residuals.
文摘We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.
