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

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