The inner engine of the high-energy emission of long gamma-ray bursts

It has been recently shown that the observed GeV emission can be explained by an electrodynamical process occurring in the “inner engine” of a BdHN: a rotating BH of mass M and angular momentum per unit mass a, embedded in very-low-density ionized plasma and a test, ordered magnetic field, asymptotically aligned with the BH rotation axis and of strength B₀. The electric field induced by the magnetic field and the BH rotation, modeled by the Papapetrou-Wald (1974)solution of the Einstein-Maxwell equations, accelerates charged particles of the surrounding ionized plasma in the vicinity of the BH. We show that indeed the electrons accelerate to ultrarelativistic energies radiating high-energy photons. In particular: 1) along the BH rotation axis the electrons can gain up to 10¹⁸ eV, implying that GRBs may contribute to the observed ultrahigh-energy cosmic rays; 2) the GeV emission is emitted in a “cone” with approximate semi-aperture angle of 60°, centered on the BH rotation axis; 3) higher energies can be emitted only near to the BH rotation axis at very small angles. For instance, for inner engine fiducial parameters M= 4 M_⊙,a / M=0.3, and B₀= 10¹¹ G, a power of the order of 10⁵⁰ erg s⁻¹ is radiated off in the GeV energy domain.