Transverse conductivity of a relativistic plasma in oblique electric and magnetic fields

Resistive tearing is a primary candidate for flares occurring in stressed magnetic fields. Its possible application to the strongly magnetized environments (H_z ∼ 10¹² G) near the surface of neutron stars, particularly as a mechanism for generating the plasma heating and particle acceleration leading to gamma-ray bursts, has motivated a quantum treatment of this process, which requires knowledge of the electrical conductivity σ of a relativistic gas in a new domain, i.e., that of a low-density (n_e) plasma in oblique electric [E = (0, E_y, E_z)] and magnetic fields. We discuss the mathematical formalism for calculating σ and present numerical results for the range of parameter values 10⁹ ≤ H_z ≤ 10¹² G, E_z/H_z ≲ 10^-4, E_y ≲ 10^-4H_z²/£2, and 10²⁰ ≤ n_e ≤ 10²⁵ cm^-3. Our results indicate that σ depends very strongly on both the applied electric and magnetic fields, and that σ ∼ E_z² E_z/H_z² over this range.