A note on the relationship between solutions of Einstein, Ramanujan and Chazy equations

Details A note on the relationship between solutions of Einstein, Ramanujan and Chazy equations A note on the relationship between solutions of Einstein, Ramanujan and Chazy equations

2011-02-22

arxiv.org/abs/1102.4456v2

Physics

General Physics

Some clarifications added, references added and misprints corrected, to be published in IJTP

Scientific paper

10.1007/s10773-011-0996-3

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 imporatant role in the number theory. Using the known solutions of the Ramanujan and Chazy equations, we find the corresponding solutions of the Einstein equation. The relationship between the Friedmann equation and the equations of the trefoil knot and figure-eight knot is established.

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