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Regular black holes sourced by nonlinear electrodynamics

Kirill A. Bronnikov

Submitted on 1 November 2022

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=FμνFμν or on two variables: either L(f,h), where h=FμνFμν, where Fμν is the Hodge dual of Fμν, or L(f,J), where J=FμνFνρFρσFσμ. 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 qe0 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 qm0. 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.

Preprint

Comment: 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)

Subjects: General Relativity and Quantum Cosmology; Astrophysics - High Energy Astrophysical Phenomena; High Energy Physics - Theory

URL: http://arxiv.org/abs/2211.00743

The behavior of $A(r)$ according to \eqn {A-ch} with $m =1$ and $q =0.9,\ 1.06,\ 1.2$ (bottom-up).