Regular black holes sourced by nonlinear electrodynamics

2022/11/01 by К. А. Бронников, Kirill A. Bronnikov, Bronnikov, Kirill A. · 16 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Theory (hep-th) #Pulsars and Gravitational Waves Research #astro-ph.HE #gr-qc #hep-th

paper · pdf · doi:10.48550/arxiv.2211.00743

30 pages, 4 figures. Invited chapter for the edited book "Regular Black Holes: Towards a New Paradigm of the Gravitational Collapse'' (Ed. C. Bambi, Springer Singapore, expected in 2023)

arxiv created 2022/11/01 · openalex publication_date 2022/11/01 · arxiv updated 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is a brief review on the existence and basic properties of static, spherically symmetric regular black hole solutions of general relativity, where the source of gravity is represented by nonlinear electromagnetic fields with the Lagrangian function L depending on the single invariant f = F_μνF^μν or on two variables: either L(f, h), where h = ^*F_μν F^μν, where ^*F_μν is the Hodge dual of F_μν, or L(f, J), where J = F_μνF^νρ F_ρσ F^σμ. A number of no-go theorems are discussed, revealing the conditions under which the space-time cannot have a regular center, among which the theorems concerning L(f,J) theories are probably new. These results concern both regular black holes and regular particlelike or starlike objects (solitons) without horizons. Thus, a regular center in solutions with an electric charge q_e≠ 0 is only possible with nonlinear electrodynamics (NED) having no Maxwell weak field limit. Regular solutions with L(f) and L(f, J) NED, possessing a correct (Maxwell) weak-field limit, are possible if the system contains only a magnetic charge q_m ≠ 0. It is shown, however, that in such solutions the causality and unitarity as well as dynamic stability conditions are inevitably violated in a neighborhood of the center. Some particular examples are discussed.

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