Dear Ryoji Furui,
I have a comment about your referenced paper "Energy and Spacetime". At the beginning of section 4 on page 3 you give a formula for the "total relativistic energy of M" and show that momentum is not conserved. If a graviton acts like a photon on absorption then the formula is wrong and should be E = m_o p = gamma m_o to conserve momentum.
The first couple of pages of this material on collisions which is taken from a text on relativity by A.P. French explains the details. I particularly like French's rationally skeptical attitude towards the conservation laws, calling them 'statements' instead.
It may be that a graviton is essentially different and your formula is correct. It seems to me the only reason to call your formula (which is a standard one) "wrong" is that it does not conserve momentum. At any rate, I found your idea that there is an oscillation between material and non-material energy very interesting and something worth playing with.
Best regards,
Colin