Relativistic Gravity and the Origin of Inertia and InertialMass: An important topic for the explanation of darkmatter and dark energy

If equilibrium is to be a frame-independent condition, it is necessary the gravitational force to have precisely the same transformation law as that of the Lorentz-force. Therefore, gravity should be described by a gravitomagnetic theory with equations which have the same mathematical form as those of the electromagnetic theory, with the gravitational mass as a Lorentz invariant. Using this gravitomagnetic theory, in order to ensure the relativity of all kinds of translatory motion, we accept the principle of covariance and the equivalence principle and thus we prove that, 1. The external inertial force, perceived by an accelerating body, is real gravitational force due to induction effects from the entire Universe. 2. The internal inertial force, depends on the body's internal structure, but in a free fall it is canceled because of the equivalence principle and the body experiences only the external inertial force. That is why all bodies, fall with the same acceleration. 3. The inertial mass of a body depends on the distribution of matter in the Universe and this seems very important for the explanation of dark matter and dark energy. 4. The gravitational field affects the spacetime metric and all the freely moving bodies follow geodesic of the metric. 5. We can obtain the Schwarzschild metric and thus, the new theory is in agreement with all past experiments and observations.