On regular black strings spacetimes in nonlinear electrodynamics

TL;DR

This paper explores the coupling of General Relativity with Nonlinear Electrodynamics to analyze the possibility of regular black string solutions, establishing fundamental constraints and constructing new regular solutions with finite curvature invariants.

Contribution

It extends no-go theorems to cylindrical symmetries, proving regular electric black strings cannot be generated by NED, and provides explicit regular black string solutions with regular cores.

Findings

Regular, purely electric black strings cannot be generated by NED with Maxwell limit.

Constructed new exact solutions for regular black strings with finite curvature invariants.

Demonstrated that these solutions satisfy causality and unitarity constraints.

Abstract

In this work, we investigate the coupling of General Relativity with Nonlinear Electrodynamics (NED), governed by a general Lagrangian $\mathcal{L}(\mathcal{F})$, to address the axial singularity of four-dimensional black strings. Through a model-independent analysis, we scrutinize the viability of regular configurations by extending no-go theorems, originally formulated for spherical spacetimes, to cylindrical symmetries. We provide a comprehensive mathematical proof that regular, purely electric black strings cannot be generated by any NED Lagrangian that recovers the Maxwell limit in the weak-field regime, establishing a fundamental constraint for cylindrical topologies. Despite these limitations, we employ specific mathematical frameworks to construct new exact solutions for black strings, including cylindrical analogues of the well-known Bardeen and Hayward regular black hole classes. Each solution is analytically derived, and we demonstrate that their curvature invariants remain finite everywhere, effectively replacing the axial singularity with a regular core. Furthermore, we evaluate the physical consistency of these new metrics by subjecting them to stringent causality and unitarity constraints. Our results provide a comprehensive classification of the conditions under which NED can regularize cylindrical spacetimes and offer new insights into how topological differences between spherical and axial symmetries influence the global structure and the physical viability of non-singular gravitational objects in nonlinear gauge theories.