Ernst Equation
   HOME

TheInfoList



OR:

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: \Re(u)(u_+u_r/r+u_) = (u_r)^2+(u_z)^2. where \Re(u) is the real part of u. 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 {{theoretical-physics-stub