Impact of Scientific Computing on Science and Society

0575320 - MÚ 2024 RIV CH eng M - Část monografie knihy
Křížek, Michal
On extreme computational complexity of the Einstein equations.
Impact of Scientific Computing on Science and Society. 1. Cham: Springer, 2023 - (Neittaanmäki, P.; Rantalainen, M.), s. 3-23. Computational Methods in Applied Sciences, 58. ISBN 978-3-031-29081-7
Grant CEP: GA ČR(CZ) GA23-06159S
Institucionální podpora: RVO:67985840
Klíčová slova: Einstein equations * Schwarzschild solution * finite difference method
Obor OECD: Pure mathematics
https://doi.org/10.1007/978-3-031-29082-4_1

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.
Trvalý link: https://hdl.handle.net/11104/0345111