Bañados-Silk-West phenomenon for near-fine-tuned particles with an external force: General classification of scenarios

If two particles moving toward a black hole collide in the vicinity of the horizon, the energy <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>E</a:mi><a:mrow><a:mi mathvariant="normal">c</a:mi><a:mo>.</a:mo><a:mi mathvariant="normal">m</a:mi><a:mo>.</a:mo></a:mrow></a:msub></a:math> in the center-of-mass frame can grow indefinitely if one of the particles is fine-tuned. This is the Bañados-Silk-West (BSW) effect. One of the objections against this effect is that, for some types of horizon, fine-tuned particles cannot reach the horizon. However, this difficulty can be overcome if, instead of exact fine-tuning, one particle is nearly fine-tuned, with the value of small detuning being adjusted to the distance to the horizon. Such particles are called near-fine-tuned. We give classification of such particles and describe possible high-energy scenarios of collision in which they participate. We analyze the ranges of possible motion for each type of particle and determine under which condition such particles can reach the horizon. We analyze collision energy <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>E</e:mi><e:mrow><e:mi mathvariant="normal">c</e:mi><e:mo>.</e:mo><e:mi mathvariant="normal">m</e:mi><e:mo>.</e:mo></e:mrow></e:msub></e:math> and determine under which conditions it may grow indefinitely. We also take into consideration the forces acting on particles and find when the BSW effect with nearly fine-tuned particles is possible with finite forces. We demonstrate that the BSW effect with particles under discussion is consistent with the principle of kinematic censorship. According to this principle, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>E</i:mi><i:mrow><i:mi mathvariant="normal">c</i:mi><i:mo>.</i:mo><i:mi mathvariant="normal">m</i:mi><i:mo>.</i:mo></i:mrow></i:msub></i:math> cannot be literally infinite in any event of collision (if no singularity is present), although it can be made as large as one likes.