Penrose and super-Penrose energy extraction from a Reissner-Nordström black hole spacetime with a cosmological constant through the Bañados-Silk-West mechanism

The Penrose process, a process that transfers energy from a black hole to infinity, together with the Ba\~nados-Silk-West (BSW) mechanism, a mechanism that uses collisions of ingoing particles at the event horizon of a black hole to locally produce large amounts of energy, is studied in a combined description for a $d$ dimensional extremal Reissner-Nordstr"om black hole spacetime with negative, zero, or positive cosmological constant, i.e., for an asymptotically anti-de Sitter (AdS), flat, or de Sitter (dS) spacetime. This blending of the Penrose process with BSW collisions is an instance of a collisional Penrose process. In an electrically charged extremal Reissner-Nordstr"om black hole background, in the vicinity of the event horizon, several types of radial collisions between electrically charged particles can be considered, the most interesting one is between a critical particle, i.e., a particle that has its electric charge adjusted in a specific way to the other relevant parameters, and a usual particle, as it gives a divergent center of mass frame energy locally. A divergent center of mass frame energy at the point of collision is a favorable condition to extract energy from the black hole, but not sufficient, since, e.g., the product particles might go down the hole. So, to understand whether energy can be extracted or not in a Penrose process, we investigate in detail a collision between ingoing particles 1 and 2, from which particles 3 and 4 emerge, with the possibility that particle 3 can carry the energy extracted far out from the black hole horizon, i.e., there is a high Killing energy transported by particle 3. One finds that the mass, the energy, the electric charge, and the initial direction of motion of particle 3 can have different values, depending on the collision internal process itself. But, the different possible values of the parameters of the emitted particle 3 lie within some range, and moreover the energy of particle 3 can, in some cases, be arbitrarily high but not infinite, characterizing a super-Penrose process. It is also shown that particle 4 has negative energy, as required in a Penrose process, living in its own electric ergosphere while it exists, i.e., before being engulfed by the event horizon. For zero cosmological constant we find that the results do not depend on the number of dimensions, but they do for negative and positive cosmological constant. The value of the cosmological constant also introduces differences in the lower bound for the energy extracted.