The Gravitomagnetic Vector Potential and the Gravitomagnetic Field of a Rotating Sphere

Authors: Jacob Biemond

The gravitomagnetic vector potential and corresponding gravitomagnetic field generated by a rotating sphere with a homogeneous mass density are investigated. Outside the sphere both vector potential and field may coincide with the results from the ideal dipole model. For the axial gravitomagnetic field inside the sphere a new exact expression is derived. More general expressions for both vector potential and field inside the sphere are proposed and checked. Their validity is compared with series expansions for the equatorial gravitomagnetic vector potential and gravitomagnetic field. Application of Stokes’ theorem to the basic gravitomagnetic equation is compatible with the ideal dipole result for the gravitomagnetic field at the surface of the sphere. Starting from the basic gravitomagnetic equations, the validity of the general internal gravitomagnetic field is confirmed. Observations of two LAGEOS satellites, Gravity Probe B mission and planned ring-laser experiment are shortly discussed. Starting from the Maxwell equations, the present treatment can also be applied to the electromagnetic case. Analogous results are found for the electromagnetic vector potential and the electromagnetic field.

Comments: 18 Pages, including 5 figures and 1 table

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Submission history

[v1] 2012-05-15 14:18:13

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