Figure 8

Figure 8: The push-forward from a point in the th x-constituent’s three-dimensional matter space (on the left) to the corresponding “fluid-particle” worldline in spacetime (on the right). The points in matter space are labelled by the coordinates {X1x,X2x,X3x}, and the constituent index x = n,s. There exist as many matter spaces as there are dynamically independent fluids, which for this case means two.