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Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

“…Here the equality ξ β;α = −ξ α;β = −Γ γ αβ ξ γ following from the Killing equation was used, and element of an arbitrary 2-surface d S αβ is represented in the form [20] …”

Gravitomagnetic Resonance Shift Due to a Slowly Rotating Compact Star

“…If m I is the inertial mass of the test particle then in addition to the binding force −m I ω 2 0 r , the damping force −m I γv, and an external force F 0 exp iωt acting along, say, the x direction, there also acts on the particle a GEM force m g (G+v×H). Considering the GE field of magnitude −g to be along y-axis and the GM field of magnitude H in the direction normal to the xy-plane [13], we find that the GEM force has a component m g Hv y in the x direction and a component −m g Hv x in the y direction; where v x and v y are the components of velocity in the x and y directions respectively. With these additional terms and the fact that m g = m I (= m), in accordance with the general theory of relativity, we get the equations of motion as a coupled system of ordinary differential equations…”

“…Acknowledgments I am grateful to to Dr. B. J. Ahmedov for bringing to my attention reference [13], and for various comments. I also thank Dr. A. Qadir for many useful conversations.…”

General Relativistic Shift in Plasma Frequency due to a Slowly Rotating Compact Star

“…In this case the components of H are (0, 0, H ), therefore effective components of the gravitomagnetic force lie in the xy-plane. We take, without loss of generality, the xy-plane to be the equatorial plane of the star [8,9].…”