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Structure of the spacetime under gravitation obtained by purely dynamical method

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By comparing the special relativistic motion of a planet with respect to the sun and that of the sun to the planet, it is concluded that the spatial and time… Click to show full abstract

By comparing the special relativistic motion of a planet with respect to the sun and that of the sun to the planet, it is concluded that the spatial and time scales in the spacetime under the gravitation of the sun, or generally of a mass, are different from those in the inertial system. Meanwhile, it is argued that the inertial space around a mass is not the space at rest with respect to the mass but such a space as falling to or escaping from the mass with a certain acceleration depending on the distance from the mass. Taking into account the difference of the spatial and time scales between the inertial and the non-inertial systems around the sun and the mutually accelerating motion of both systems, the line element is calculated in the spacetime under the gravitation of the sun. The line element thus obtained is the same as that of Schwarzschild.

Keywords: gravitation; structure spacetime; mass; spacetime gravitation; sun; gravitation obtained

Journal Title: General Relativity and Gravitation
Year Published: 2019

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