Abstract
Einstein’s special theory of relativity was a great breakthrough in our understanding of the physical world, but it presented a problem: it was incompatible with Newton’s law of gravitation. Newton himself, and some ten generations of physicists and astronomers that followed, used this law to describe the motion of planets with remarkable accuracy. Granted, there was a tiny discrepancy in the calculated precession rate of the orbit of Mercury, but it did not seem to be a cause for concern. After all, theories seldom agree with all the data at any given time. Some of the data may simply be wrong and some discrepancies are later explained away with more careful theoretical analysis. Thus, Newton’s theory appeared rock solid. However, it did not fit into the framework of special relativity.
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- 1.
The volume of a 3D spherical space is analogous to the area of a regular 2D sphere. Notice that this volume is different from the volume enclosed by a sphere in 3D Euclidean space \(V_{E} = \frac{4}{3}\pi r^{3}\).
- 2.
GR gives the same formula Eq. (4.2) for the Schwarzschild radius as our Newtonian derivation.
- 3.
This discovery earned Joseph H. Taylor and Russell A. Hulse the 1993 Nobel Prize in physics.
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Perlov, D., Vilenkin, A. (2017). The Fabric of Space and Time. In: Cosmology for the Curious. Springer, Cham. https://doi.org/10.1007/978-3-319-57040-2_4
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DOI: https://doi.org/10.1007/978-3-319-57040-2_4
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