Nonequatorial tachyon trajectories in Kerr space-time and the second law of black-hole physics

The behavior of tachyon trajectories (spacelike geodesics) in Kerr space-time is discussed. It is seen that the trajectories may be broadly classified into three types according to the magnitude of the angular momentum of the tachyon. When the magnitude of angular momentum is large [$\mathrm{}\left|h\right|\mathrm{}\ge a{(1+{\Gamma }^2)}^{\frac{1}{2}}$, where $h$ and $\Gamma$ are the angular momentum and energy at infinity and $a=\frac{S}{M}$ the angular momentum and mass of a rotating black hole] the incoming tachyon from infinity necessarily has a bounce for $r>\mathrm{}0\mathrm{}$. In the other cases, a negative value for Carter's constant of motion $Q$ is permitted, which happens to be a necessary condition for the tachyon to fall into the singularity. Next, the second law of black-hole physics is investigated in the general case of nonequatorial trajectories. It is shown that nonequatorial tachyons can decrease the area of the Kerr black hole only if it is rotating sufficiently rapidly [$a>\left(\frac{4}{3\surd 3}\right)M$].