Ernst equation

Today, Ernst equation has become a fundamental issue in modern society, generating a great impact in different areas of our lives. Whether in the technological, social, political or economic sphere, Ernst equation has managed to influence our decisions and the way we perceive the world around us. With the constant advancement of technology and globalization, Ernst equation has become a reference point to understand the complexity of our interactions and how they affect our reality. In this article, we will explore the impact of Ernst equation on today's society and how it has shaped the way we think and act in the world we inhabit.

Mathematical equation used to find exact solutions of equations in the general theory of relativity

Not to be confused with Nernst equation.

In mathematics, the Ernst equation is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst [Wikidata].

The Ernst equation

The equation reads:

$${\displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.}$$

For its Lax pair and other features see e.g. 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

1. ^ Weisstein, Eric W, Ernst equation, MathWorld--A Wolfram Web.
2. ^ "Biography of Frederick J. Ernst". Archived from the original on 2018-01-04. Retrieved 2017-05-09.
3. ^ Harrison, B. Kent (30 October 1978). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters. 41 (18). American Physical Society (APS): 1197–1200. Bibcode:1978PhRvL..41.1197H. doi:10.1103/physrevlett.41.1197. ISSN 0031-9007.
4. ^ Marvan, M. (2004). Recursion operators for vacuum Einstein equations with symmetries. Proceedings of the Conference on Symmetry in nonlinear mathematical physics. Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. Vol. 50. Kyiv, Ukraine. pp. 179–183. arXiv:nlin/0401014.

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