Figure 1 . Notation on a picture: let the circle in red represent the closed spacelike submanifold (cid:16) . Then, pick up any future-pointing vector ~n orthogonal to (cid:16) at a given point q 2 (cid:16) and launch the unique geodesic (cid:13) tangent to ~n at q , represented here by the blue dotted line. The geodesic vector (cid:12)eld tangent to (cid:13) is then represented by ~N . If f ~e A g is a basis of vectors tangent to (cid:16) at q , ~E A denote the vector (cid:12)elds de(cid:12)ned by parallel propagating ~e A along (cid:13) . For further details, refer to the main text and