Super Penrose Process for Kerr Black Hole And White Hole in Rainbow Gravity

Recently, O.B.Zaslavskii considers the collision near the horizon of the extremal Kerr black hole that produces two particles and one of two particles has divergent conserved killing energy(the so called super Penrose process). O.B.Zaslavskii shows this particle can not move in a asymptotic region in this universe. This means super Penrose process for extremal Kerr black hole is impossible. However, recently, Mandar Patil and Tomohiro Harada show this particle can enter event horizon, turns back and emerges through white hole event horizon into asymptotic region in other universe. This means super Penrose process for extremal Kerr white hole is possible. During this progress, they assume this high energy particle's trajectory is geodesic in Kerr background. However, according to rainbow gravity, an unbounded energy particle will change the spacetime background and observe different effective space-time geometries. Furthermore, this particle's angular momentum is slightly less than the max value which particle can enter black hole. Therefore, when one considers rainbow gravity, this particle with unbounded energy may not enter black hole. In this paper, we will consider rainbow gravity's effect. We will show for some rainbow functions, there is a critical energy. If particle's energy is greater than it, particle will not enter black hole and turn back. It means super Penrose process for extremal Kerr white hole becomes impossible in some rainbow gravity. Because of this high energy particle turning back, the super Penrose process for extremal Kerr black hole becomes possible. Therefore, we see the possibility of super Penrose process for Kerr black hole or white hole depends on rainbow gravity.