Gravitational Wave and Spiral Galaxy (Gravito Radiative Force)

Abstract

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 ø ⁱ_j are negligible.