Einstein-Euler-Heisenberg Theory and charged black holes

Understand

Taking into account the Euler-Heisenberg effective Lagrangian of one-loop nonperturbative quantum electrodynamics (QED) contributions, we formulate the Einstein-Euler-Heisenberg theory and study the solutions of nonrotating black holes with electric and magnetic charges in spherical geometry.

• In the limit of strong and weak electromagnetic fields of black holes, we calculate the black hole horizon radius, area, and total energy up to the leading order of QED corrections and discuss the black hole irreducible mass, entropy, and maximally extractable energy as well as the Christodoulou-Ruffini mass formula.
• We find that these black hole quantities receive the QED corrections, in comparison with their counterparts in the Reissner-Nordstr\"om solution.
• The QED corrections show the screening effect on black hole electric charges and the paramagnetic effect on black hole magnetic charges.