Show that, for radial motion along the polar (0= 0) axis, the Kerr metrie is d s^{2}=-\left(1-\frac{r_{s} r}{r^{2}+a^{2}}\right) d t^{2}+d r^{2} /\left(1-\frac{r_{s} r}{r^{2}+a^{2}}\right) Identify any singularities in the metric, and in each case say whether it is a coordinate singularity or a physical one.(4) Find the t and r equations of motion for a particle in free-fall motion along the-polar axis, using the behaviour as r→ o to identify any conserved quantities.Hence show that if the particle is released from rest at large r, the r equation of motion is \frac{d r}{d \tau}=\pm\left(\frac{r_{s} r}{r^{2}+a^{2}}\right)^{1 / 2} Solve the equation of motion in part (b) for r(T) where |r| << a, and hence describe what happens to the particle at r= 0.(3)