Vacuum breakdown around a Kerr black hole surrounded by a magnetic field

¹ Department of Science and Technology for Sustainable Development and One Health, Università Campus Bio-Medico di Roma, Via Alvaro del Portillo 21, I-00128 Rome, Italy
² ICRANet, Piazza della Repubblica 1, I-65122 Pescara, Italy
³ Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
⁴ ICRA, Dipartimento di Fisica, Sapienza Università di Roma, I-00185 Rome, Italy
⁵ ICRANet-Ferrara, Dip. di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
⁶ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
⁷ INAF, Istituto de Astrofisica e Planetologia Spaziali, Via Fosso del Cavaliere 100, I-00136 Rome, Italy
⁸ INAF, Viale del Parco Mellini 84, I-00136 Rome, Italy

^⋆ Corresponding author: jorge.rueda@icra.it

Received: 15 July 2025
Accepted: 27 October 2025

Abstract

We present the invariant characterization of the region where vacuum breakdown into electron-positron (e⁺e⁻) pairs occurs due to an overcritical electric field, the dyadoregion, in the case of a Kerr black hole (BH) in the presence of an external, asymptotically uniform test magnetic field aligned with the BH rotation axis, using the Wald solution. We calculated the dyadoregion morphology, the electromagnetic energy available for the pairs, the pair-creation rate, the number density of pairs, the average energy per pair, and their energy density and pressure. These results provide initial conditions for simulating the subsequent dynamics of the pair-produced plasma and astrophysical applications in the context of high-energy transients involving BHs in strong electromagnetic fields.