Abstract
The first exact nontrivial solution of Einstein’s (vacuum) field equations (2.160i) was obtained by Schwarzschild [231]. This solution turned out to be very important in regard to experimental verifications of the theory of general relativity.
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Notes
- 1.
The line element in this form is found in (14) of Schwarzschild’s original paper [231].
- 2.
It should be noted that sometimes the domain 0 < r < 2m of the metric (3.9) also goes by this name.
- 3.
To derive (3.77vii,viii), use the following equations for a symmetric tensor S jk : \({\nabla }_{j}{S}_{\;k}^{j} = \left (1/\sqrt{\vert g\vert }\right ) \cdot {\partial }_{j}\left (\sqrt{\vert g\vert }\cdot {S}_{k}^{j}\right ) -\frac{1} {2} \cdot \left ({\partial }_{k}{g}_{ij}\right ) \cdot {S}^{ij}\).
- 4.
Counterexamples for nonconvex domains are provided in [61].
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Das, A., DeBenedictis, A. (2012). Spherically Symmetric Space-Time Domains. In: The General Theory of Relativity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3658-4_3
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