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(2*M)/R[r]]) + x^2*(1 + 2*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])) + 2*beta*M*x*(x^2 + \ y^2 + z^2)*(1 - 2*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]))*R[r]^6 + beta*x*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r]^7))/((1 - beta^2)^(3/2)*r^4*R[r]^3*(C^2 - 2*M*R[r]^3 + \ R[r]^4))), (y*(beta*C*(C*(y^2 + z^2 + x^2*(1 + 5*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ 2*(y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]] - 3*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ beta*M*x*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^3 + (beta*M*(x^2 + y^2 + z^2)*(-2 + 3*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ 3*C*x*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^6 - beta*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r]^7))/ (r^4*R[r]*Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + \ R[r]^4))/(beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta^2*C^2*(-y^2 - z^2) + \ 2*beta*(-(C*x) + beta*M*(x^2 + y^2 + z^2))*R[r]^3 - beta^2*(x^2 + y^2 + \ z^2)*R[r]^4 + R[r]^6)), (z*(beta*C*(C*(y^2 + z^2 + x^2*(1 + 5*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ 2*(y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]] - 3*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ beta*M*x*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^3 + (beta*M*(x^2 + y^2 + z^2)*(-2 + 3*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ 3*C*x*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^6 - beta*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r]^7))/ (r^4*R[r]*Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + \ R[r]^4))/(beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta^2*C^2*(-y^2 - z^2) + \ 2*beta*(-(C*x) + beta*M*(x^2 + y^2 + z^2))*R[r]^3 - beta^2*(x^2 + y^2 + \ z^2)*R[r]^4 + R[r]^6))}, {(y*(beta*C*(C*(y^2 + z^2 + x^2*(1 + 5*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ 2*(y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]] - 3*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ beta*M*x*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^3 + (beta*M*(x^2 + y^2 + z^2)*(-2 + 3*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ 3*C*x*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^6 - beta*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r]^7))/ (r^4*R[r]*Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + \ R[r]^4))/(beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta^2*C^2*(-y^2 - z^2) + \ 2*beta*(-(C*x) + beta*M*(x^2 + y^2 + z^2))*R[r]^3 - beta^2*(x^2 + y^2 + \ z^2)*R[r]^4 + R[r]^6)), (Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + \ R[r]^4))/(beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta*C^2*x*(x^2 + y^2 + \ z^2 + (x^2 + y^2 + z^2)*(-2 + Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - (x^2 - 2*y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ R[r]^3*(-2*beta*M*x*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]]) + C*(x^2 + x^2*(-1 + Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + (-2*y^2 + \ z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + beta*x*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r])))/(Sqrt[1 - beta^2]*r^4*(C^2 - 2*M*R[r]^3 + R[r]^4)), (-3*C*y*z*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]*(-(beta*C*x) + \ R[r]^3)*Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + R[r]^4))/ (beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)])/ (Sqrt[1 - beta^2]*r^4*(C^2 - 2*M*R[r]^3 + R[r]^4))}, {(z*(beta*C*(C*(y^2 + z^2 + x^2*(1 + 5*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ 2*(y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]] - 3*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ beta*M*x*(x^2 + y^2 + z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^3 + (beta*M*(x^2 + y^2 + z^2)*(-2 + 3*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - \ 3*C*x*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]])*R[r]^6 - beta*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r]^7))/ (r^4*R[r]*Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + \ R[r]^4))/(beta^2*C^2*(r - x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + \ z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta^2*C^2*(-y^2 - z^2) + \ 2*beta*(-(C*x) + beta*M*(x^2 + y^2 + z^2))*R[r]^3 - beta^2*(x^2 + y^2 + \ z^2)*R[r]^4 + R[r]^6)), (-3*C*y*z*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]*(-(beta*C*x) + \ R[r]^3)* Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + R[r]^4))/(beta^2*C^2*(r - \ x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)])/(Sqrt[1 - beta^2]*r^4*(C^2 \ - 2*M*R[r]^3 + R[r]^4)), (Sqrt[((-1 + beta^2)*R[r]^2*(C^2 - 2*M*R[r]^3 + R[r]^4))/(beta^2*C^2*(r - \ x)*(r + x) + 2*beta*(C*x - beta*M*(x^2 + y^2 + z^2))*R[r]^3 + beta^2*(x^2 + y^2 + z^2)*R[r]^4 - R[r]^6)]*(beta*C^2*x*(x^2 + y^2 + \ z^2 + (x^2 + y^2 + z^2)*(-2 + Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) - (x^2 + y^2 - 2*z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + \ R[r]^3*(-2*beta*M*x*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]]) + C*(x^2 + x^2*(-1 + Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + (y^2 - \ 2*z^2)*Sqrt[1 + C^2/R[r]^4 - (2*M)/R[r]]) + beta*x*(x^2 + y^2 + z^2)*(-1 + Sqrt[1 + C^2/R[r]^4 - \ (2*M)/R[r]])*R[r])))/(Sqrt[1 - beta^2]*r^4*(C^2 - 2*M*R[r]^3 + R[r]^4))}}\ \>", "\<\ 2 2 2 3 \ 4 (-1 + beta ) R[r] (C - 2 M R[r] + \ R[r] ) {{-((Sqrt[--------------------------------------------------------------------\ --------------------------------------] 2 2 2 2 2 \ 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + z )) \ R[r] + beta (x + y + z ) R[r] - R[r] 2 \ 2 2 2 2 2 2 2 2 C \ 2 M 2 2 2 C 2 M (beta (-(C x (3 (x + y + z ) + (x + y + z ) (-2 - 5 Sqrt[1 + \ ----- - ----]) + 3 (2 x + y + z ) Sqrt[1 + ----- - ----])) - \ 4 R[r] 4 R[r] R[r]\ R[r] 2 \ 2 2 2 4 C 2 M 2 2 2 \ 2 2 2 C 2 M 3 2 beta M r x Sqrt[1 + ----- - ----] + beta C M (x + y + z ) \ (3 x + y + z ) Sqrt[1 + ----- - ----]) R[r] + 4 R[r] \ 4 R[r] R[r] \ R[r] 2 \ 2 2 3 4 C 2 M 4 2 2 2 2 \ 2 C 2 M 2 C 2 M beta M r x Sqrt[1 + ----- - ----] R[r] + (C (-x - y - z - (y \ + z ) (-1 + Sqrt[1 + ----- - ----]) + x (1 + 2 Sqrt[1 + ----- - ----])) + 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 \ 2 2 2 2 C 2 M 6 \ 2 2 2 C 2 M 7 2 beta M x (x + y + z ) (1 - 2 Sqrt[1 + ----- - ----])) R[r] \ + beta x (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r] )) / 4 R[r] \ 4 R[r] R[r] \ R[r] 2 3/2 4 3 2 3 4 ((1 - beta ) r R[r] (C - 2 M R[r] + R[r] ))), (y (beta C 2 \ 2 2 2 2 2 C 2 M 2 2 \ C 2 M 2 2 2 C 2 M (C (y + z + x (1 + 5 Sqrt[1 + ----- - ----]) + 2 (y + z ) Sqrt[1 \ + ----- - ----] - 3 (x + y + z ) Sqrt[1 + ----- - ----]) - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 \ 2 2 2 2 2 C 2 M 3 \ 2 2 2 C 2 M C 2 M \ 6 beta M x (x + y + z ) Sqrt[1 + ----- - ----]) R[r] + (beta M (x \ + y + z ) (-2 + 3 Sqrt[1 + ----- - ----]) - 3 C x Sqrt[1 + ----- - ----]) \ R[r] - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 2 2 2 C 2 M 7 beta (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r] )) / 4 R[r] R[r] 2 2 2 \ 3 4 4 (-1 + beta ) R[r] (C - 2 M \ R[r] + R[r] ) (r R[r] \ Sqrt[-------------------------------------------------------------------------\ ---------------------------------] 2 2 2 2 \ 2 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + \ z )) R[r] + beta (x + y + z ) R[r] - R[r] 2 2 2 2 2 2 2 3 \ 2 2 2 2 4 6 (beta C (-y - z ) + 2 beta (-(C x) + beta M (x + y + z )) R[r] - \ beta (x + y + z ) R[r] + R[r] )), 2 \ 2 2 2 2 2 C 2 M 2 2 \ C 2 M 2 2 2 C 2 M (z (beta C (C (y + z + x (1 + 5 Sqrt[1 + ----- - ----]) + 2 (y + z ) \ Sqrt[1 + ----- - ----] - 3 (x + y + z ) Sqrt[1 + ----- - ----]) - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 \ 2 2 2 2 2 C 2 M 3 \ 2 2 2 C 2 M C 2 M \ 6 beta M x (x + y + z ) Sqrt[1 + ----- - ----]) R[r] + (beta M (x \ + y + z ) (-2 + 3 Sqrt[1 + ----- - ----]) - 3 C x Sqrt[1 + ----- - ----]) \ R[r] - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 2 2 2 C 2 M 7 beta (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r] )) / 4 R[r] R[r] 2 2 2 \ 3 4 4 (-1 + beta ) R[r] (C - 2 M \ R[r] + R[r] ) (r R[r] \ Sqrt[-------------------------------------------------------------------------\ ---------------------------------] 2 2 2 2 \ 2 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + \ z )) R[r] + beta (x + y + z ) R[r] - R[r] 2 2 2 2 2 2 2 3 \ 2 2 2 2 4 6 (beta C (-y - z ) + 2 beta (-(C x) + beta M (x + y + z )) R[r] - \ beta (x + y + z ) R[r] + R[r] ))}, 2 \ 2 2 2 2 2 C 2 M 2 2 \ C 2 M 2 2 2 C 2 M {(y (beta C (C (y + z + x (1 + 5 Sqrt[1 + ----- - ----]) + 2 (y + z ) \ Sqrt[1 + ----- - ----] - 3 (x + y + z ) Sqrt[1 + ----- - ----]) - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 \ 2 2 2 2 2 C 2 M 3 \ 2 2 2 C 2 M C 2 M \ 6 beta M x (x + y + z ) Sqrt[1 + ----- - ----]) R[r] + (beta M (x \ + y + z ) (-2 + 3 Sqrt[1 + ----- - ----]) - 3 C x Sqrt[1 + ----- - ----]) \ R[r] - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 2 2 2 C 2 M 7 beta (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r] )) / 4 R[r] R[r] 2 2 2 \ 3 4 4 (-1 + beta ) R[r] (C - 2 M \ R[r] + R[r] ) (r R[r] \ Sqrt[-------------------------------------------------------------------------\ ---------------------------------] 2 2 2 2 \ 2 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + \ z )) R[r] + beta (x + y + z ) R[r] - R[r] 2 2 2 2 2 2 2 3 \ 2 2 2 2 4 6 (beta C (-y - z ) + 2 beta (-(C x) + beta M (x + y + z )) R[r] - \ beta (x + y + z ) R[r] + R[r] )), 2 2 2 3 \ 4 (-1 + beta ) R[r] (C - 2 M R[r] + \ R[r] ) (Sqrt[---------------------------------------------------------------------\ -------------------------------------] 2 2 2 2 2 \ 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + z )) R[r] \ + beta (x + y + z ) R[r] - R[r] 2 \ 2 2 2 2 2 2 2 2 C 2 M \ 2 2 2 C 2 M (beta C x (x + y + z + (x + y + z ) (-2 + Sqrt[1 + ----- - ----]) \ - (x - 2 y + z ) Sqrt[1 + ----- - ----]) + 4 R[r] \ 4 R[r] R[r] \ R[r] 2 \ 2 2 3 2 2 2 C 2 M \ 2 2 C 2 M 2 2 C 2 M R[r] (-2 beta M x (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) + C \ (x + x (-1 + Sqrt[1 + ----- - ----]) + (-2 y + z ) Sqrt[1 + ----- - ----]) \ + 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 2 2 2 C 2 M \ 2 4 2 3 4 beta x (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r]))) / \ (Sqrt[1 - beta ] r (C - 2 M R[r] + R[r] )), 4 R[r] R[r] 2 C 2 M 3 -3 C y z Sqrt[1 + ----- - ----] (-(beta C x) + R[r] ) Sqrt[ 4 R[r] R[r] 2 2 2 3 \ 4 (-1 + beta ) R[r] (C - 2 M R[r] + \ R[r] ) -----------------------------------------------------------------------\ -----------------------------------] 2 2 2 2 2 3 \ 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + z )) R[r] \ + beta (x + y + z ) R[r] - R[r] ---------------------------------------------------------------------------\ ------------------------------------------------------------------------------\ ------------- 2\ 4 2 3 4 Sqrt[1 - beta \ ] r (C - 2 M R[r] + R[r] ) 2 \ 2 2 2 2 2 C 2 M 2 \ 2 C 2 M 2 2 2 C 2 M }, {(z (beta C (C (y + z + x (1 + 5 Sqrt[1 + ----- - ----]) + 2 (y + \ z ) Sqrt[1 + ----- - ----] - 3 (x + y + z ) Sqrt[1 + ----- - ----]) - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 \ 2 2 2 2 2 C 2 M 3 \ 2 2 2 C 2 M C 2 M \ 6 beta M x (x + y + z ) Sqrt[1 + ----- - ----]) R[r] + (beta M (x \ + y + z ) (-2 + 3 Sqrt[1 + ----- - ----]) - 3 C x Sqrt[1 + ----- - ----]) \ R[r] - 4 R[r] \ 4 R[r] 4 R[r] R[r] \ R[r] R[r] 2 2 2 2 C 2 M 7 beta (x + y + z ) (-1 + Sqrt[1 + ----- - ----]) R[r] )) / 4 R[r] R[r] 2 2 2 \ 3 4 4 (-1 + beta ) R[r] (C - 2 M \ R[r] + R[r] ) (r R[r] \ Sqrt[-------------------------------------------------------------------------\ ---------------------------------] 2 2 2 2 \ 2 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + \ z )) R[r] + beta (x + y + z ) R[r] - R[r] 2 2 2 2 2 2 2 3 \ 2 2 2 2 4 6 (beta C (-y - z ) + 2 beta (-(C x) + beta M (x + y + z )) R[r] - \ beta (x + y + z ) R[r] + R[r] )), 2 C 2 M 3 -3 C y z Sqrt[1 + ----- - ----] (-(beta C x) + R[r] ) Sqrt[ 4 R[r] R[r] 2 2 2 3 \ 4 (-1 + beta ) R[r] (C - 2 M R[r] + \ R[r] ) -----------------------------------------------------------------------\ -----------------------------------] 2 2 2 2 2 3 \ 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + z )) R[r] \ + beta (x + y + z ) R[r] - R[r] ---------------------------------------------------------------------------\ ------------------------------------------------------------------------------\ ------------- 2\ 4 2 3 4 Sqrt[1 - beta \ ] r (C - 2 M R[r] + R[r] ) 2 2 2 3 \ 4 (-1 + beta ) R[r] (C - 2 M R[r] \ + R[r] ) , (Sqrt[------------------------------------------------------------------\ ----------------------------------------] 2 2 2 2 2 \ 3 2 2 2 2 4 6 beta C (r - x) (r + x) + 2 beta (C x - beta M (x + y + z )) \ R[r] + beta (x + y + z ) R[r] - R[r] 2 \ 2 2 2 2 2 2 2 2 C 2 M \ 2 2 2 C 2 M (beta C x (x + y + z + (x + y + z ) (-2 + Sqrt[1 + ----- - ----]) \ - (x + y - 2 z ) Sqrt[1 + ----- - ----]) + 4 R[r] \ 4 R[r] R[r] \ R[r] 2 \ 2 2 3 2 2 2 C 2 M \ 2 2 C 2 M 2 2 C 2 M R[r] (-2 beta M x 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