ModMax black holes in Kalb-Ramond gravity: Electric Penrose, circular orbits and collisions of electrically charged particles

We investigate electrically and magnetically charged black holes sourced by modified Maxwell (ModMax) nonlinear electrodynamics (NED) within the framework of Kalb-Ramond (KR) gravity, focusing on the horizon structure, the circular motion of charged particles, energy extraction via the Penrose process, and particle collisions. By solving the coupled field equations, we briefly derive the exact ModMax-KR black hole solution and demonstrate how the nonlinearity parameter γ and the torsion parameter ℓ influence the event and Cauchy horizons. Positive values of ℓ and γ enlarge the horizons and increase the extremal charge. The circular motion of electrically charged particles in the equatorial plane is explored through the effective potential method. We show that the innermost stable circular orbit (ISCO) radius is highly sensitive to the competition between gravitational attraction, centrifugal repulsion, and Coulomb forces. Positively charged particles undergo outward ISCO shifts due to electrostatic repulsion, while negatively charged particles are drawn inward by Coulomb attraction. The parameters γ and ℓ further regulate these effects, altering the energy and angular momentum required for circular orbits. We extend the analysis to the electric Penrose process and demonstrate that the energy-extraction efficiency is enhanced by negative γ and positive ℓ, thereby making ModMax-KR black holes more efficient energy extractors than the standard Reissner-Nordström (RN) case. Finally, we analyze collisional processes and determine that both γ and ℓ can significantly enhance the center-of-mass energy of particle collisions near the horizon.