About Gravitomagnetism
  The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms. 
Behrooz Malekolkalami and Mehrdad Farhoudi