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- Title
A Note on the Relationship Between Solutions of Einstein, Ramanujan and Chazy Equations.
- Authors
Esmakhanova, Kuralay; Myrzakulov, Yerlan; Nugmanova, Gulgasyl; Myrzakulov, Ratbay
- Abstract
The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in this simple metric case is sometime a hard job. Therefore, it is useful to construct solutions of the Einstein equation using a known solutions of some other equations which are equivalent or related to the Einstein equation. In this work, we establish the relationship the Einstein equation with two other famous equations namely the Ramanujan equation and the Chazy equation. Both these two equations play an important role in the number theory. Using the known solutions of the Ramanujan and Chazy equations, we find the corresponding solutions of the Einstein equation.
- Subjects
METAPHYSICAL cosmology; NUMERICAL solutions to Einstein field equations; MATRICES (Mathematics); NUMBER theory; MATHEMATICAL physics; MATHEMATICAL analysis
- Publication
International Journal of Theoretical Physics, 2012, Vol 51, Issue 4, p1204
- ISSN
0020-7748
- Publication type
Article
- DOI
10.1007/s10773-011-0996-3