Equation Icon  8N&tidle; ′′ [G ] = (1 − 2ξ)2 (G ′ G ′ + G ′ G ′) + 4ξ2 (G ′ ′ G + G G ′′) abc d ;cb ;d a ;ca ;d b ;cd ;ab ;abcd − 2ξ (1 − 2ξ)(G;bG;c′ad′ + G;a G;c′bd′ + G;d′ G;abc′ + G;c′ G;abd′) +2 ξ (1 − 2ξ)(G G R ′ ′ + G ′ G ′ R ) 2 ;a ;b cd ;c ;d2 ab 2 − 4ξ (G;abRc′d′ + G;c′d′ Rab )G + 2ξ Rc ′d′ RabG , (77 ) [( ) ] ′ 1 p′ ( p′ p′) 8 &tidle;Nab[G ] = 2 (1 − 2ξ ) 2ξ − -- G;p′bG; a + ξ G;b G;p′a + G;a G;p′b [( ) 2 ] 1- p′ ( p′ p′) − 4ξ 2ξ − 2 G; G;abp′ + ξ G;p′ G;ab + G G;abp′ 2 ′ − (m [+( ξR )[()1 − 2ξ)G;aG;b − 2G ξ G;]ab] 1 p′ p′ 2 ′ 2 +2 ξ 2ξ − -- G;p′ G; + 2G ξ G;p′ Rab − (m + ξR )ξ Rab G , (78 ) 2 ( ) &tidle; 1- 2 p′q 2( p′ q p q′) 8N [G ] = 2 2ξ − 2 G;p′q G; + 4ξ G;p′ G;q + G G;p q′ ( ) ( ) +4 ξ 2 ξ − 1- G G ′pq′ + G p′ G q ′ 2 ;p ;q ; ;q p ( 1) [( ) ( ) ] − 2ξ − -- m2 + ξR G;p′ G;p′ + m2 + ξR ′ G;pG;p [ 2 ] ( 2 ) p′ ( 2 ′) p − 2ξ m + ξR G;p′ + m + ξR G;p G 1 ( 2 )( 2 ′) 2 + -- m + ξR m + ξR G . (79 ) 2