In principle, the description of a relativistic particle in a gravitational eld involves General Relativity. We will nevertheless approximate this description in Special Relativity, assuming the Lagrangian of the WIMP to be L = Lu V, with L0 = g the Lagrangian of a free relativistic WIMP of mass mx, and V = CmTm the gravitational potential energy. qr = 1/1/1 \"2 is the Lorentz factor. We consider the WIMP heading on towards the centre of the neutron star. Its velocity is then just 1: = 1". Show that. T? + "r1" = F (r) where F (r) is a mction of r to be determined (give its expression}