Weyl-type Fields with Geodesic Lines of Force

Details Weyl-type Fields with Geodesic Lines of Force Weyl-type Fields with Geodesic Lines of Force

1999-05-18

arxiv.org/abs/gr-qc/9905060v1

J.Math.Phys. 40 (1999) 2032-2045

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, RevTex

Scientific paper

The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have $m>|e|$ or $m<|e|$, but cannot be in the Majumdar-Papapetrou class (in which $m = |e|$). It is algebraically general and has flat equipotential surfaces.

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