Abstract
In this chapter we analyze a model of the universe proposed by Karl Schwarzschild. In the literature, this model is presented in many equivalent ways. Here we adopt an approach that in our opinion is less formal. However, in Sect. 14.4 we introduce a definition that allows a comparison with another usual presentation of Schwarzschild’s model.
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Notes
- 1.
See [92], p. 61.
- 2.
It is evident that if a Killing vector fields exists on a spacetime \(V_{4}\), that is, the infinitesimal generator of a one-parameter group of global transformations, then \(V_{4}\) has all the properties listed in Definition 14.1.
- 3.
All the following computations can be carried out with the notebook Geometry.nb written in Mathematica.
- 4.
The reader may refer to the notebook Geometry.nb.
- 5.
In other words, we are considering the propagation of light in the absence of gravitation.
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Romano, A., Mango Furnari, M. (2019). Schwarzschild’s Universe. In: The Physical and Mathematical Foundations of the Theory of Relativity. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27237-1_14
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DOI: https://doi.org/10.1007/978-3-030-27237-1_14
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