Purely from covariance requirements regarding the special theory ofrelativity, we show that a moving body necessarily generates a gravitationalmagnetic field. Then, from the Lorentz transformations, we deduce the exactformul{\ae} describing these gravitomagnetic fields in a flat spacetime. Acomparison between our theory and the linearized theory of general relativity,concerning the gravitomagnetic effects, is briefly discussed. Next, we showthat in our theory the gravitational mass should be regarded as an invariantquantity in the same foot as the electric charge, which leads to thedifferential equations satisfied by the gravitomagnetic fields that proved tobe similar to the Maxwell equations. This allowed us to show as well thatgravitational waves indeed spread out with the speed of light. We also presentarguments showing that the vector potential can be associated to the momentumof interaction between the matter and the fields and the energy and momentumstored in the gravitomagnetic fields are also discussed. We highlight that nothing is assumed from the electromagnetic theory in ourapproach, nevertheless we found that both theories indeed have many propertiesin common, which is explained by the relativistic covariance character of boththeories. Gravitation and electromagnetism are, however, different phenomena ofnature and we finish the paper discussing some similarities and differencesbetween them.
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