Gravitational wave

New field

Notation

${\Phi }^{\mu \nu }=h^{\mu \nu }-\frac{1}{2}{\eta }^{\mu \nu }h$

(2-4)

${\Phi }^{\mu \nu }=h^{\mu \nu }-\frac{1}{2}{{\eta }^{\prime }}^{\mu \nu }h$

(3-1)

Field equation

${\partial }_{\lambda }{\partial }^{\lambda }{\Phi }^{\mu \nu }=-\kappa T^{\mu \nu }$

(2-5)

${\partial }_{\lambda }{\partial }^{\lambda }{\Phi }^{\mu \nu }+e{\Phi }^{\mu \nu }=-\kappa T^{\mu \nu }$

(3-2)

gauge condition

${\partial }_{\mu }{\Phi }^{\mu \nu }=0$ (Hilbert)

(2-6)

${\partial }_{\mu }{\Phi }^{\mu \nu }=0$ (Hilbert-like)

(3-3)