Examples
Noteworthy individual non-null electrovacuum solutions include:
- Reissner–Nordström electrovacuum (which describes the geometry around a charged spherical mass),
- Kerr–Newman electrovacuum (which describes the geometry around a charged, rotating object),
- Melvin electrovacuum (a model of a cylindrically symmetric magnetostatic field),
- Garfinkle–Melvin electrovacuum (like the preceding, but including a gravitational wave traveling along the axis of symmetry),
- Bertotti–Robinson electrovacuum: this is a simple spacetime having a remarkable product structure; it arises from a kind of "blow up" of the horizon of the Reissner-Nordström electrovacuum,
- Witten electrovacuums (discovered by Louis Witten, father of Edward Witten).
Noteworthy individual null electrovacuum solutions include:
- the monochromatic electromagnetic plane wave, an exact solution which is the general relativitistic analogue of the plane waves in classical electromagnetism,
- Bell–Szekeres electrovacuum (a colliding plane wave model).
Some well known families of electrovacuums are:
- Weyl–Maxwell electrovacuums: this is the family of all static axisymmetric electrovacuum solutions; it includes the Reissner-Nordström electrovacuum,
- Ernst–Maxwell electrovacuums: this is the family of all stationary axisymmetric electrovacuum solutions; it includes the Kerr-Newman electrovacuum,
- Beck–Maxwell electrovacuums: all nonrotating cylindrically symmetric electrovacuum solutions,
- Ehlers–Maxwell electrovacuums: all stationary cylindrically symmetric electrovacuum solutions,
- Szekeres electrovacuums: all pairs of colliding plane waves, where each wave may contain both gravitational and electromagnetic radiation; these solutions are null electrovacuums outside the interaction zone, but generally non-null electrovacuums inside the interaction zone, due to the non-linear interaction of the two waves after they collide.
Many pp-wave spacetimes admit an electromagnetic field tensor turning them into exact null electrovacuum solutions.
Read more about this topic: Electrovacuum Solution
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