Gravitomagnetic interaction of a Kerr black hole with a magnetic field as the source of the jetted GeV radiation of gamma-ray bursts

We show that the gravitomagnetic interaction of a Kerr black hole (BH) with a surrounding magnetic field induces an electric field that accelerates charged particles to ultra-relativistic energies in the vicinity of the BH. Along the BH rotation axis, these electrons/protons can reach energies of even thousands of PeV, so stellar-mass BHs in long gamma-ray bursts (GRBs) and supermassive BHs in active galactic nuclei (AGN) can contribute to the ultrahigh-energy cosmic rays (UHECRs) thorough this mechanism. At off-axis latitudes, the particles accelerate to energies of hundreds of GeV and emit synchrotron radiation at GeV energies. This process occurs within $60^\circ$ around the BH rotation axis, and due to the equatorial-symmetry, it forms a double-cone emission. We outline the theoretical framework describing these acceleration and radiation processes, how they extract the rotational energy of the Kerr BH and the consequences for the astrophysics of GRBs.