In mathematics, the Ernst equation is an
integrable non-linear partial differential equation, named after the American
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
.
The Ernst equation
The equation reads:
where
is the real part of
. For its
Lax pair and other features see e.g.
and references therein.
Usage
The ''Ernst equation'' is employed in order to produce exact solutions of the
Einstein's equations in the
general theory of relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physi ...
.
References
Partial differential equations
General relativity
Integrable systems
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