After developing his Special Theory of Relativity (1905), which does not include gravity in its considerations, Einstein spent the next ten years developing an all-encompassing General Theory of Relativity that does include gravity and essentially describes, in a series of 10 equations, how matter in the Universe on the scale of planets, stars, and galaxies behaves. A basic assumption is made about the Universe itself on the largest scales, namely that it is homogeneous, so that roughly it is the same everywhere regarding its mass and energy, and it should also be isotropic in that it should look basically the same in all directions. For such a Universe, the EFE can be summarized in the beautiful expressionwhere Guv (the Einstein tensor) encodes information regarding the curvature of spacetime and Tuv (energy-momentum tensor) describes the distribution of matter and energy. The subscripts u, v run through the indices 0, 1, 2, 3 where the first index represents time and the other three represent the three spatial dimensions. The EFE describe the curvature of spacetime due to the presence of mass and energy.

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The Universe

  • Joel L. Schiff

摘要

After developing his Special Theory of Relativity (1905), which does not include gravity in its considerations, Einstein spent the next ten years developing an all-encompassing General Theory of Relativity that does include gravity and essentially describes, in a series of 10 equations, how matter in the Universe on the scale of planets, stars, and galaxies behaves. A basic assumption is made about the Universe itself on the largest scales, namely that it is homogeneous, so that roughly it is the same everywhere regarding its mass and energy, and it should also be isotropic in that it should look basically the same in all directions. For such a Universe, the EFE can be summarized in the beautiful expressionwhere Guv (the Einstein tensor) encodes information regarding the curvature of spacetime and Tuv (energy-momentum tensor) describes the distribution of matter and energy. The subscripts u, v run through the indices 0, 1, 2, 3 where the first index represents time and the other three represent the three spatial dimensions. The EFE describe the curvature of spacetime due to the presence of mass and energy.