Solutions and basic properties of regularized Maxwell theory

Abstract

The regularized Maxwell theory is a recently discovered theory of non-linear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique non-linear electrodynamics (that depends only on the field invariant $F_{\mu \nu }{F}^{\mu \nu }$) whose radiative solutions can be found in the Robinson--Trautman class. At the same time, it is the only electrodynamics of this type (apart from Maxwell) whose slowly rotating solutions are fully characterized by the electrostatic potential. In this paper, after discussing the basic properties of the regularized Maxwell theory, we concentrate on its spherical electric solutions. These not only provide `the simplest' regularization of point electric field and its self-energy, but also feature complex thermodynamic behavior (in both canonical and grandcanonical ensembles) and admit an unprecedented phase diagram with multiple first-order, second-order, and zeroth-order phase transitions. Among other notable solutions, we construct a novel C-metric describing accelerated AdS black holes in the regularized Maxwell theory. We also present a generalization of the regularized Maxwell Lagrangian applicable to magnetic solutions, and find the corresponding spherical, slowly rotating, and weakly NUT charged solutions.

19 pages, 18 figures v2: published version - title change due to PRD regulations

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• Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography
• Light rings and causality for nonsingular ultracompact objects sourced by nonlinear electrodynamics
• Thermodynamics of Regular Black Holes in Anti-de Sitter Space
• Thermodynamics of charged and accelerating black holes
• Well-posed non-vacuum solutions in Robinson--Trautman geometry
• Topological Signatures and Geometrothermodynamics of Critical Phenomena in Regularized Maxwell Black Holes
• Hexadecapole at the heart of nonlinear electromagnetic fields
• Thermodynamics and the Joule-Thomson expansion of dilaton black holes in 2+1 dimensions