Abstract
General relativity (GR) is an extension of Einstein’s special theory of relativity (SR), which was required in order to include observers in non-trivial gravitational backgrounds.
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Notes
- 1.
Of course the choice \(\mathrm {diag}(+1,-1,-1,-1)\) is equally valid but we will have occasion later to restrict our attention to the spacial part of the metric, in which case a positive (spatial) line-element is cleaner to work with.
- 2.
Strictly speaking it is a pseudo-metric, as the distance it measures between two distinct points can be zero.
- 3.
The presence of the energy-momentum tensor is related to the fact that it is not merely the mass of matter that creates gravity, but its momentum, as required to maintain consistency when transforming between various Lorentz-boosted frames.
- 4.
This argument is taken from Chap. 8 of [2], where a more detailed discussion can be found.
References
R.M. Wald, General Relativity (The University of Chicago Press, 1984)
D. Koks, Explorations in Mathematical Physics: The Concepts Behind an Elegant Language (Springer, 2006)
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Vaid, D., Bilson-Thompson, S. (2017). Classical GR. In: LQG for the Bewildered. Springer, Cham. https://doi.org/10.1007/978-3-319-43184-0_2
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DOI: https://doi.org/10.1007/978-3-319-43184-0_2
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