Nonstatic Analogs of Schwarzschild's Interior Solution in General Relativity

The theory of relativity shows that the times measured by two observers will in general be different if they are in relative motion, so that their respective times between any two coincidences will differ. Bergmann [1] has investigated the problem of a particle moving in a small simple harmonic motion in a static gravitational field, and has found that the time difference for this particle and an observer at rest becomes zero whenever the particle passes through the centre and limits of its swing. This problem will now be dealt with in a different manner, using Schwarzschild's interior solution of the gravitational equations. The exterior solution for a point mass is not suitable in the present case, due to the singularity of the field at a point in the path of the particle.

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Static Axisymmetric Interior Solution in General Relativity

Physical Review ◽

10.1103/physrev.163.1373 ◽

1967 ◽

Vol 163 (5) ◽

pp. 1373-1376 ◽

Cited By ~ 14

Author(s):

J. J. J. Marek

Keyword(s):

General Relativity ◽

Interior Solution

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On rotating charged dust in general relativity. V

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1983.0110 ◽

1983 ◽

Vol 389 (1797) ◽

pp. 291-298 ◽

Cited By ~ 8

Keyword(s):

General Relativity ◽

Maxwell Equations ◽

Interior Solution ◽

Charged Dust ◽

Exterior Solution ◽

Cylindrically Symmetric

We find an exact cylindrically symmetric stationary exterior solution of the Einstein-Maxwell equations. We then match this solution smoothly onto an interior solution for rotating charged dust found earlier by the author. The solution thus obtained is regular and well behaved inside the matter. Such matched solutions are rare either for the Einstein or Einstein-Maxwell equations. Some properties of the solution are discussed.

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A charged interior solution with cosmological constant Λ in general relativity

Physics Letters A ◽

10.1016/0375-9601(88)90400-8 ◽

1988 ◽

Vol 130 (1) ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Chongming Xu ◽

Chun Li Shen ◽

Xuejun Wu

Keyword(s):

General Relativity ◽

Cosmological Constant ◽

Interior Solution

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Solution of a Spherically Symmetric Static Problem of General Relativity for an Elastic Solid Sphere

Applied Physics Research ◽

10.5539/apr.v9n6p8 ◽

2017 ◽

Vol 9 (6) ◽

pp. 8 ◽

Cited By ~ 2

Author(s):

Valery V. Vasiliev ◽

Leonid V. Fedorov

Keyword(s):

General Relativity ◽

Elastic Solid ◽

Static Problem ◽

Solid Sphere ◽

Theory Of Elasticity ◽

Relativity Theory ◽

Interior Solution ◽

Spherically Symmetric ◽

Complementary Energy ◽

Linear Elastic

The paper is concerned with the spherically symmetric static problem of the General Relativity Theory (GRT). The classical interior solution of this problem found in 1916 by K. Schwarzschild for a fluid sphere is generalized for a linear elastic isotropic solid sphere. The GRT equations are supplemented with the equation for the stresses which is similar to the compatibility equation of the theory of elasticity and is derived using the principle of minimum complementary energy for an elastic solid. Numerical analysis of the obtained solution is undertaken.

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