Suppose a 2-dimensional space is spanned by the coordinates (v, x) and that the line
element is defined by:
ds2 = -xdv2 + 2dvdx
i) assuming that the nature and properties of the spacetime line element still hold,
show that a particle in the negative x-axis can never venture into the positive
x-axis. that is, show that a particle becomes trapped if it travels into the
negative x-axis.
ii) draw a representative light cone that illustrates how a particle is trapped.