  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.
