Charged Dilation Black Holes as Particle Accelerators

We examine the possibility of arbitrarily high energy in the Center-of-mass(CM) frame of colliding neutral particles in the vicinity of the horizon of a charged dilation black hole(BH). We show that it is possible to achieve the infinite energy in the background of the dilation black hole without fine-tuning of the angular momentum parameter. It is found that the CM energy $({\cal E}_{cm})$ of collisions of particles near the infinite red-shift surface of the extreme dilation BHs are arbitrarily large while the non-extreme charged dilation BHs have the finite energy. We have also compared the ${\cal E}_{cm}$ at the horizon with the ISCO(Innermost Stable Circular Orbit) and MBCO (Marginally Bound Circular Orbit) for extremal Reissner-Nordstr{\o}m(RN) BH and Schwarzschild BH. We find that for extreme RN BH the inequality becomes ${\cal E}_{cm}\mid_{r_{+}}>{\cal E}_{cm}\mid_{r_{mb}}> {\cal E}_{cm}\mid_{r_{ISCO}}$ i.e. ${\cal E}_{cm}\mid_{r_{+}=M}: {\cal E}_{cm}\mid_{r_{mb}=\left(\frac{3+\sqrt{5}}{2}\right)M} : {\cal E}_{cm}\mid_{r_{ISCO}=4M} =\infty : 3.23 : 2.6$. While for Schwarzschild BH the ratio of CM energy is ${\cal E}_{cm}\mid_{r_{+}=2M}: {\cal E}_{cm}\mid_{r_{mb}=4M} : {\cal E}_{cm}\mid_{r_{ISCO}=6M} = \sqrt{5} : \sqrt{2} : \frac{\sqrt{13}}{3}$. Also for Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) BHs, the ratio is being ${\cal E}_{cm}\mid_{r_{+}=2M}: {\cal E}_{cm}\mid_{r_{mb}=2M} : {\cal E}_{cm}\mid_{r_{ISCO}=2M} =\infty : \infty : \infty$.