Static and stationary solutions of the Einstein-Maxwell equations

1979 ◽  
Vol 10 (8) ◽  
pp. 681-697 ◽  
Author(s):  
F. I. Cooperstock ◽  
V. de la Cruz
Keyword(s):  
Maxwell Equations ◽  
Stationary Solutions

A class of exact interior solutions of the Einstein-Maxwell equations

1977 ◽  
Vol 353 (1675) ◽  
pp. 523-531 ◽  
Keyword(s):  
Angular Velocity ◽  
Laplace Equation ◽  
Maxwell Equations ◽  
Flat Space ◽  
Stationary Solutions ◽  
Constant Angular Velocity ◽  
Arbitrary Solution ◽  
Charged Matter ◽  
Axis Of Symmetry ◽  
Interior Solutions

A class of exact interior stationary solutions of the Einstein-Maxwell equations is found in terms of an arbitrary solution of the flat-space Laplace equation. These solutions represent pressure-free charged matter rotating with constant angular velocity about an axis of symmetry. Some properties of the solution are discussed.

A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

1989 ◽  
Vol 423 (1865) ◽  
pp. 379-386 ◽  
Keyword(s):  
Coordinate System ◽  
Maxwell Equations ◽  
Stationary Solutions ◽  
Einstein Vacuum Equations ◽  
Static Solutions ◽  
Maxwell Space ◽  
Einstein Vacuum ◽  
One To One ◽  
The One ◽  
Vacuum Space

A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-centre problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons.

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