The great teacher John Archibald Wheeler has passed away. His group’s legacy can be summarized by the massive rendition on the subject of general relativity in the book “Gravitation” by Kip Thorne et al. The book influenced and inspired many great minds of the modern scientific world. The following quote is his view on gravitomagnetism. 
From this quote, one can see his strong conviction that there must be gravitomagnetism in the mechanical universe.
However, being a great teacher did not always go along with being a great innovator. James Maxwell was one of the examples. He is not known as being a great teacher. Maybe Albert Einstein was another one. It seems that the brain of a human being can not be both ways. Either it can be deeply innovative inside his/her soul or widely interactive with other human beings.
His long search for the true gravitomagnetism in general relativity has not resulted in the finding of dipole gravity, the true gravitomagnetism. It is tragic in a way. But this event may have been predicted by Nostradamus 500 years ago.
The reason for the persistent effort in search of the true gravitomagnetism was obviously to find a way to counteract gravity, the eternal yoke all living things have to endure. By having gravitomagnetism, we have a repulsive gravity which can negate the unstoppable pulling effect of gravity. It means the ultimate freedom of physical bodies. If we are lucky, it may also be possible to explain the so far unexplained cosmological phenomena, ie, the jets and the dark matter problems, which have been considered possible failures of general relativity in the large scale universe.
Because of the delay in the finding of the true gravitomagnetism, so far, we had many independent branches of theories to deal with this unending enigma. Finally, Wheeler’s vision of the true gravitomagnetism has been fulfilled by the theory of dipole gravity.
This is the end of the old era and the beginning of the new era in the science of gravitation.
Theory of Gravitation, Cosmology and a part of general relativity