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INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE LOCATION PARAMETERS OF spherically SYMMETRIC DISTRIBUTIONS

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Chinese Science Bulletin 1989年第7期34卷 533-537页

作者：范剑青方开泰 Institute of Applied Mathematics Academia Sinica Beijing

I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are pr... 详细信息

关键词： inadmissibility minimax estimator quadratic loss spherically symmetric distributions.

A Model for a spherically Symmetric Space Generated by a Spherical Gravitational Source and a Gravitational Medium with Constant Mass Density

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International Journal of Astronomy and Astrophysics 2013年第2期3卷 21-27页

作者： Nikolaj N. Popov Vladimir I. Tsurkov Dorodnitsyn Computing Center Russian Academy of Sciences Moscow Russia

A metric on a spherically symmetric space generated by a spherical source of gravity and filled with a gravitational medium is constructed, and criteria for the continuity of this metric on the entire space (which is equivalent to the absence of black holes) are found. Properties of radial geodesics under various constraints on the size of the gravitational source, its mass, and the mass density of the gravitational medium are studied.

关键词： spherically Symmetric Space with Discontinuous Scalar Curvature Generalized Schwarzschild Metric Radial Geodesic Black Hole Dark Energy

Modified Tunneling Radiation of Fermions from a spherically Symmetric Spacetime with Dark Matter

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Journal of Applied Mathematics and Physics 2015年第8期3卷 931-936页

作者： Zhongwen Feng Xiaotao Zu School of Physical Electronics University of Electronic Science and Technology of China Chengdu China

In the paper, we use the generalized Dirac equation to study the Hawking temperature and entropy of a spherically symmetric spacetime with the dark matter. The results show that the dark matter can influence the thermodynamic properties of the black hole. Meanwhile, we find the GUP corrected temperature and entropy are not only determined by the nature of black but also related to the properties of tunneling particles. Besides, the GUP can slow down the increase of Hawking temperature and causes the remnants.

关键词： Generalized Uncertainty Principle spherically Symmetric Spacetime Dark Matter

Mathematical Model of Relativistic Anisotropic Compact Stellar Model Admitting Linear Equation of State

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Communications in Theoretical Physics 2018年第11期69卷 585-592页

作者： Sumita Banerjee Department of Mathematics Budge Budge Institute of Technology

In present paper, a static, spherically symmetric, anisotropic stellar object has been discussed by assuming a linear relationship between the matter density ρ and radial pressure pr. The interior solution is continuously matched with the exterior Schwarzschild vacuum solution at the junction interface. Various physical features viz. energy conditions,mass-radius relationship, stability are analyzed for our stellar model. By assigning some particular value to the arbitrary constants we have obtained a model of compact star of radius 6.7 km. and mass 1.148 M_⊙, which is very close to the observational data of the compact star Her X-1 proposed by Rawls et al. [Rawls, et al., Astrophys. J. 730(2011) 25].We have obtained that the model satisfies all the regularity conditions. We have found that our proposed model is stable as well as singularity-free.

关键词： compact anisotropic spherically symmetric singularity free

Black Holes or Dark Stars—What Follows from the General Relativity Theory

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Journal of Modern Physics 2017年第7期8卷 1087-1100页

作者： Valery V. Vasiliev Institute of Problems in Mechanics Russian Academy of Sciences Moscow Russia

The paper is concerned with spherically symmetric static problem of the Classical Gravitation Theory (CGT) and the General Relativity Theory (GRT). First, the Dark Stars, i.e. the objects that are invisible because of high gravitation preventing the propagation of light discovered in the 18th century by J. Michel and P. Laplace are discussed. Second, the Schwarzchild solution which was obtained in the beginning of the 20th century for the internal and external spaces of the perfect fluid sphere is analyzed. This solution results in singular metric coefficients and provides the basis of the Black Holes. Third, the general metric form in spherical coordinates is introduced and the solution of GRT problem is obtained under the assumption that gravitation does not affect the sphere mass. The critical sphere radius similar to the Black Hole horizon of events is found. In contrast to the Schwarzchild solution, the radial metric coefficient for the sphere with the critical radius referred to as the Dark Star is not singular. For the sphere with radius which is less than the critical value, the GRT solution becomes imaginary. The problem is discussed within the framework of the phenomenological theory which does not take into account the actual microstructure of the gravitating objects and, though the term “star” is used, the analysis is concerned with a model fluid sphere rather than with a real astrophysical object.

关键词： General Relativity spherically Symmetric Problem Black Holes Dark Stars

Linearized Equations of General Relativity and the Problem of Reduction to the Newton Theory

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Journal of Modern Physics 2020年第2期11卷 221-236页

作者： Valery V. Vasiliev Leonid V. Fedorov Institute of Problems in Mechanics Russian Academy of Sciences Moscow Russia

The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.

关键词： General Relativity Gravitation Constant Linearized Equations spherically Symmetric Problem

To the Schwarzschild Solution in General Relativity

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Journal of Modern Physics 2018年第14期9卷 2482-2494页

作者： Valery V. Vasiliev Leonid V. Fedorov Institute of Problems in Mechanics Russian Academy of Sciences Moscow Russia

The paper is concerned with the history of the spherically symmetric static problem solution of General Relativity found in 1916 by K. Schwarzschild [1] [2] which is interpreted in modern physics as the background of the objects referred to as Black Holes. First, the modern interpretation this solution which does not exactly coincide with original solution obtained by K. Schwarzschild is discussed. Second, the basic equations of the original Schwarzschild solution are presented in modern notations allowing us to compare existing and original solutions. Finally, a modification of the Schwarzschild approach is proposed allowing us to arrive at the exact solution of the Schwarzschild problem.

关键词： General Relativity spherically Symmetric Problem Schwarzschild’s Solution Black Holes

To the Complete Set of Equations for a Static Problem of General Relativity

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Journal of Modern Physics 2019年第12期10卷 1401-1415页

作者： Valery V. Vasiliev Leonid V. Fedorov Institute of Problems in Mechanics Russian Academy of Sciences Moscow Russia

The paper is concerned with the formulation of the static problem of general relativity. As known, this problem is reduced to ten equations for the compo-nents of the Einstein tensor and the solution of these equations is associated with two principal problems. First, since the components of the Einstein tensor identically satisfy four conservation equations, only six of these equations are mutually independent. So, the set of the Einstein equations actually contains six independent equations for ten components of the metric tensor and should be supplemented with four additional equations which are missing in the original theory. Second, for a deformable solid the Einstein tensor is associated with the energy tensor which is expressed in terms of six stresses induced by gravitation. These stresses are not known and the relativity theory does not propose any equations for them. Thus, the static problem of general relativity cannot be properly formulated because the set of governing equations is not complete. In the paper, the problem of completeness of the general relativity governing set of equations is analyzed in application to the spherically symmetric static problem and the proposed approach is further described for the general case. As an example, linearized axisymmetric problem is considered.

关键词： General Relativity Coordinate Conditions Compatibility Stress Equations spherically Symmetric Problem