Einstein-Euler-Heisenberg Theory and charged black holes

TL;DR

This paper incorporates quantum electrodynamics corrections into black hole solutions, revealing how these effects modify black hole properties such as horizon size, entropy, and energy, with implications for charged black hole physics.

Contribution

It formulates the Einstein-Euler-Heisenberg theory including QED effects and analyzes their impact on nonrotating charged black holes, a novel integration of quantum corrections into classical black hole models.

Findings

QED corrections increase black hole horizon area and entropy.

QED effects cause screening of electric charges and paramagnetic behavior of magnetic charges.

Total energy and maximum extractable energy decrease due to QED corrections.

Abstract

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. As a result, the black hole horizon area, irreducible mass, and entropy increase; however, the black hole total energy and maximally extractable energy decrease, compared with the Reissner-Nordstr\"om solution. In addition, we show that the condition for extremely charged black holes is modified due to the QED correction.