Energetics of particle collisions near dirty rotating extremal black holes: Banados-Silk-West effect versus Penrose process

TL;DR

This paper investigates the energy limits of particle collisions near dirty rotating extremal black holes, showing that while high-energy collisions are possible, the energy of detectable products is limited, with implications for astrophysical observations.

Contribution

It extends previous Kerr black hole analyses to generic dirty black holes, establishing bounds on energy and mass of collision products and identifying new energy extraction scenarios.

Findings

Upper bounds on energy and mass of collision products at infinity.

Positive energy gain is possible but modest, depending on near-horizon metric parameters.

Certain energy extraction scenarios are impossible in Kerr but possible in dirty black holes.

Abstract

If two particles collide near the horizon of a rotating extremal black hole, under certain conditions the energy E_{c.m.} in the center-of-mass frame can grow without limit (the so-called Banados-Silk-West effect). We consider collisions that produce two other particles. We show that for a generic dirty (surrounded by matter) black hole, there exist upper bounds on the energy and mass of product particles which can be detected at infinity. As a result, the positive energy gain is possible but is quite modest. It mainly depends on two numbers in which near-horizon behavior of the metric is encoded. The obtained results suggest astrophysical limits on the possibility of observation of the products of the collisional Banados-Silk-West effect. These results are consistent with recent calculations for the Kerr metric, extending them to generic dirty black holes. It is shown that for dirty black holes there are types of scenarios of energy extraction impossible in the Kerr case.