Kinematic censorship as a constraint on allowed scenarios of high energy particle collisions

Abstract

In recent years, it was found that the energy $E_{c.m.}$ in the centre of mass frame of two colliding particles can be unbounded near black holes. If collision occurs exactly on the horizon, $E_{c.m.}$ is formally infinite. However, in any physically reasonable situation this is impossible. We collect different scenarios of such a kind and show why in every act of collision $E_{c.m.}$ is indeed finite (although it can be as large as one likes). The factors preventing infinite energy are diverse: the necessity of infinite proper time, infinite tidal forces, potential barrier, etc. This prompts us to formulate a general principle according to which the limits in which $E_{c.m.}$ becomes infinite are never achieved. We call this the kinematic censorship (KC). Although by itself the validity of KC is quite natural, its application allows one to forbid scenarios of collisions predicting infinite $E_{c.m.}$ without going into details. The KC is valid even in the test particle approximation, so explanation of why $E_{c.m.}$ cannot be infinite, does not require references (common in literature) to the non-linear regime, backreaction, etc. The KC remains valid not only for free moving particles but also if particles experience the action of a finite force. For an individual particle, we consider a light-like continuous limit of a time-like trajectory in which the effective mass turns into zero. We show that it cannot be accelerated to an infinite energy during a finite proper time under the action of such a force. As an example, we consider dynamics of a scalar particle interacting with a background scalar field.