Figure 7

Figure 7: The push-forward from “fluid-particle” points in the three-dimensional matter space labelled by the coordinates {X1, X2, X3 } to fluid-element worldlines in spacetime. Here, the push-forward of the “Ith” (I = 1,2,...,n) fluid-particle to, say, an initial point on a worldline in spacetime can be taken as A A i X I = X (0, xI) where i xI is the spatial position of the intersection of the worldline with the t = 0 time slice.