Ernst equation
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Short description: Mathematical equation used to find exact solutions of equations in the general theory of relativity
In mathematics, the Ernst equation[1] is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst ({{{2}}}).[2]
The Ernst equation
The equation reads: [math]\displaystyle{ \Re(u)(u_{rr}+u_r/r+u_{zz}) = (u_r)^2+(u_z)^2. }[/math]
For its Lax pair and other features see e.g. [3][4] and references therein.
Usage
The Ernst equation is employed in order to produce the exact solutions of the Einstein's equations in the general theory of relativity.
References
- ↑ Weisstein, Eric W, Ernst equation, MathWorld--A Wolfram Web.
- ↑ "Biography of Frederick J. Ernst". http://mypages.iit.edu/~segre/iit_physics_bios/ernst_f.html.
- ↑ Harrison, B. Kent (30 October 1978). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters (American Physical Society (APS)) 41 (18): 1197–1200. doi:10.1103/physrevlett.41.1197. ISSN 0031-9007. Bibcode: 1978PhRvL..41.1197H.
- ↑ Marvan, M. (2004). "Recursion operators for vacuum Einstein equations with symmetries". Proceedings of the Conference on Symmetry in nonlinear mathematical physics. 50. Kyiv, Ukraine. 179–183.
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