Naked Singularity as Accelerator for Spinning Particle

When two particles collide at the horizon of a black hole and one of them satisfies some critical conditions, the relative velocity between them can be arbitrarily large, thus the energy of the center-of-mass will reach infinity. Such a process is called BSW mechanism which can accelerate a particle to arbitrarily high energy. There are also some studies showing that a Kerr naked singularity can be more qualified as a particle accelerator for arbitrarily high energy. Previous researchers mainly concentrate on geodesic motion of particles. In this paper, we will take spinning particles which won't move along a timelike geodesic and carry more parameters into our consideration. By employing the Mathisson-Papapetrou-Dixon equation, we will prove that for a spinning particle in hyper-extremal Reissner-Nordstrom or Kerr spacetime where exists a naked singularity at $r=0$, its Effective Potential $V_{eff}=-\dot{r}^2$ must be able to reach zero within the interval $0 < r < M$, thus an ingoing particle will be able to turn back and then collide with another ingoing particle at $r=M$. If the spacetime is ${\bf slightly}$ hyper-extremal, the energy of center of mass $E_{cm}$ will be arbitrarily high.