mass-differences of particles

 Why would the pion appear to be more massive than the muon, and the muon more massive than the electron, if they are all one and the same particle? The answer : the difference is a function of the rate of rotation of the particle. Likewise, in gravitational "frame-dragging", part of the gravitational field (hence, the apparent gravitational mass) is transformed into potential for accelerating bodies bypassing in the same direction as the rotation.

The process is similar is transformation of part of a magnetic field-strength into potential for electric acceleration for free charged particles (or else, force overcoming electric resistance, in a wire), with the result of a decrease in the original field-strength; or conversely.

application of this principle to galaxies

 Why would a "great attractor" appear to be more massive than an ordinary galaxy, if they are both one and the same in nature? The answer : the difference is a function of the angular momentum (rotation * distance from centre * inertial mass). Here the proportionate difference (change) in mass is such that by far the greater part of the gravitational field is transmuted into "frame-dragging" potential.

(These are, then, all examples of differences of gravitational mass from inertial mass.)

If Einstein in his "general relativity" missed realizing the "frame-dragging" potential must be subtracted from the gravitational field, then this is a deficiency in the calculations : they differences may be too small to be noticeable for planetary rotations, but might be observable in particle or galactic rotations.