Case

Case (1): vector gauge

Case (2): scalar gauge

Case (3): conservation

Conditions

h μ ν h μ ν + ν Λ μ + μ Λ ν

h μ ν h μ ν + η μ ν Λ

μ T μ ν = 0

Relation between coefficients

1 + b = 0 (3-7)

a + b = 0 (3-8)

c + d = 0 (3-9)

e + f = 0 (3-10)

1 + 2 c + d = 0 (4-8)

a + b = 0 (4-9)

e + 2 f = 0 (4-10)

1 + b = 0 (3-12)

a + c = 0 (3-13)

b + d = 0 (3-14)

e μ h μ ν + f η μ ν μ h = 0 (3-15)

Unknown coefficients

c , d , e , f

a , b , c , d , e , f

a , c , e , f