Abstract
We show how to explicitly express the first of the 10 Einstein partial differential equations to demonstrate their extremely large general complexity. Consequently, it is very difficult to use them, for example, to realistically model the evolution of the Solar system, since their analytical solution even for at least two massive bodies is not known. Significant computational problems associated with their numerical solution are illustrated as well. Thus, we cannot verify whether the Einstein equations describe the motion of two or more bodies sufficiently accurately.
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Acknowledgements
The author is indebted to J. Brandts, A. Mészáros, L. Somer, and A. Ženíšek for inspiration and valuable suggestions. Supported by grant no. 23-06159S of the Grant Agency of the Czech Republic and RVO 67985840 of the Czech Republic.
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Křížek, M. (2023). On Extreme Computational Complexity of the Einstein Equations. In: Neittaanmäki, P., Rantalainen, ML. (eds) Impact of Scientific Computing on Science and Society. Computational Methods in Applied Sciences, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-031-29082-4_1
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