In principle, the description of a relativistic particle in a gravitational field involves General Relativity. We will nevertheless approximate this description in Special Relativity, assuming the Lagrangian of the WIMP to be L = Lo - V, with Lo = Y the Lagrangian of a free relativistic WIMP of mass my, and V = -Amx the gravitational potential energy. v = 1//1 -5 is the Lorentz factor. We consider the WIMP heading on towards the centre of the neutron star. Its velocity is then just v = . Starting from the definition of the Lorentz factor, show these two expressions: = pri/c' and 1 + 124 =