Equation Icon  ( ) g¯u¯u = − f 1 + ¯r2f ¯ℰ∗ + 𝒪 (¯r3∕ℛ3 ), (568 ) ( ) g¯u¯a = − ¯Ωa + 2¯r2f ¯ℰ∗a + ¯ℬ∗a + 𝒪 (¯r3∕ℛ3 ), (569 ) 3 ( ) ¯ ¯ 1-2 m2- ¯∗ 1- 2 ¯∗ 3 3 g ¯a¯b = δab − ΩaΩb − 3¯r 1 − 2 ¯r2 ℰ ab − 3 ¯r ℬab + 𝒪(¯r ∕ℛ ), (570 )