4 χ $^{0}$$_{1}$( x ) = χ $^{1}$$_{0}$( x ) = Δ a $^{4}$r$^{2}$(Δ − a $^{2}$) + a $^{2}$r$^{3}$(4 Mr ( M − r ) + 2 r 3 − Q $^{2}$( a 2 + 2 Mr − r $^{2}$) + Δ(2 M − r )) + r $^{6}$(Δ − a $^{2}$) [ $^{(}$2 a $^{2}$r2 + r 4 $^{)}$cosh( ζ ) $^{(}$Q 2 − Mr ) √ √ ( a 2 + r $^{2}$) 2 − a $^{2}$Δ $^{(}$( a 2 + r $^{2}$) 2 − a $^{2}$Δ $^{)}$( r ( r − 2 M ) + Q $^{2}$) + a $^{2}$( Q 2 − 2 Mr ) $_{2}$− 1 $^{(}$( a 2 + r $^{2}$) 2 − a $^{2}$Δ ) 3 / 2 [ a $^{(}$a 4 $^{(}$− $^{(}$r ( r − 3 M ) + Q 2 $^{))}$+ a 2 $^{(}$Q 2 $^{(}$a 2 + 3 Mr + Q 2 + r 2 $^{)}$+ r $^{(}$Δ( r − 3 M ) − r $^{(}$6 M 2 − 3 Mr + r 2 ) ) − Q 4 $^{)}$+ r 4 $^{(}$r ( r − 5 M ) + 3 Q 2 ) )    a cosh( ζ ) ( $^{(}$a 2 + r 2 ) 2 − a $^{2}$Δ ) $^{(}$2 Mr − Q 2 ) √ $^{(}$( a 2 + r $^{2}$) 2 − a $^{2}$Δ $^{)}$( r ( r − 2 M ) + Q $^{2}$) + a $^{2}$( Q 2 − 2 Mr ) 2 + sinh( ζ ) $^{(}$a 2 $^{(}$2 Mr − Q 2 + r 2 $^{)}$+ r 4 )    ] (15) χ $^{1}$$_{3}$( x ) = − χ $^{3}$$_{1}$( x ) √ Δ r 4 [ cosh( ζ )$^{}$  a $^{(}$2 Mr − Q 2 $^{) (}$2 a 2 $^{(}$Q 2 − Mr $^{)}$+ r 4 ) $^{√}$( a 2 + r $^{2}$) 2 − a $^{2}$δ + 2 a $^{(}$Mr − Q 2 )   √ √ ( a 2 + r $^{2}$) 2 − a $^{2}$Δ $^{(}$( a 2 + r $^{2}$) 2 − a $^{2}$δ $^{)}$( − 2 Mr + Q 2 + r $^{2}$) + a $^{2}$( Q 2 − 2 Mr ) 2 + sinh( ζ ) $^{(}$a 2 $^{(}$2 Mr − Q 2 + r 2 $^{)}$+ r 4 ) ] (16) The LLT is defined by Eq.(14), where m is taken to be the mass of the particle species under con- sideration. This is an infinitesimal LLT since λ$_{ab}$ = − λ$_{ba}$ . The LLT then turns out to have only four nonvanishing terms which can be sepa- rated in to two symmetries, δ a b + λ $^{a}$$_{b}$( x ) dτ , which corresponds to a unitary operator that acts on the state of the particle. This operator changes the spin, in particular it acts like the unitary matrix U in The explicit expressions are lengthy and so are represented graphically in Fig.(1) for some aver- age parameters of a Kerr-Newman black hole. This turns out to also be a boost along the 1-axis and a rotation about the 2-axis, as in Schwarzschild black hole case. With constant momentum p $^{a}$( x ) = ( m cosh ( ζ ) , 0 , 0 , m sinh ( ζ )) pointing in the 3-axis, the change of the spin be- comes a rotation as follows. After an infinitesimal proper time dτ , the par- ticle moves in the 3-axis by an amount, δφ = u $^{ϕ}$dτ . Over this the momentum in the local in- ertial frame transforms under the LLT, Λ $^{a}$$_{b}$( x ) = as in [9], where W ( x ) = W (Λ ( x ) , p ( x )) = L − $^{1}$(Λ p ) Λ L ( p ) is a local Wigner rotation. It follows that W $^{a}$$_{b}$( x ) = W $^{a}$$_{b}$(Λ ( x ) , p ( x )) = $^{[}$L − $^{1}$(Λ p ) Λ L ( p ) ] $^{a}$$_{b}$, with a standard Lorentz transform (LT) L $^{a}$$_{b}$( p ) defined by, U (Λ ( x )) | p $^{a}$( x ) , σ ; x 〉 = ∑ σ ′ D (1 / 2) σ $^{′}$σ ( W ( x )) | Λ p $^{a}$( x ) , σ $^{′}$; x 〉 , (18) L $^{0}$$_{0}$( p ) = γ, L $^{0}$$_{i}$( p ) = L $^{i}$$_{0}$( p ) = p i m , L i k ( p ) = δ$_{ik}$ + ( γ − 1) p $^{i}$pk | − → p | $_{2}$, (19) λ $^{0}$$_{1}$( x ) = λ $^{1}$$_{0}$( x ) λ $^{1}$$_{3}$( x ) = − λ $^{3}$$_{1}$( x ) (17)