Gravitational Wave and Spiral Galaxy (Gravito Radiative Force)

Einstein[1] proposed a general relativistic wave equation, which reduces to $$ \left( {{\nabla ^2} - {{\left( {{\partial \over {c\partial t}}} \right)}^2}} \right)\phi _i^j = {{16\pi G} \over {{c^4}}}T_i^j, $$ (1) when we introduce gravitational potentials through $$ {g_{00}} = 1 - {1 \over 2}({\phi _{00}} + {\phi _{11}} + {\phi _{22}} + {\phi _{33}}), $$ (2) $$ {g_{11}} = 1 - {1 \over 2}({\phi _{00}} + {\phi _{11}} - {\phi _{22}} - {\phi _{33}}), $$ (3) $$ {g_{22}} = - 1 - {1 \over 2}({\phi _{00}} - {\phi _{11}} + {\phi _{22}} - {\phi _{33}}), $$ (4) $$ {g_{33}} = - 1 - {1 \over 2}({\phi _{00}} - {\phi _{11}} - {\phi _{22}} + {\phi _{33}}), $$ (5) and $$ {g_{01}} = {\phi _{01}},{g_{12}} = {\phi _{12}},etc., $$ (6) and assume that $$ {{\partial \phi _j^i} \over {\partial {x^i}}} = 0 $$ (7) and that all quantities nonlinear in o j i are negligible.