# Constraints on singularity resolution by nonlinear electrodynamics

**Authors:** Ana Bokulić, Tajron Jurić, Ivica Smolić  
**arXiv:** [2206.07064](https://arxiv.org/abs/2206.07064)  
**Date:** 2022-06-14  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2206.07064v1/

## Key points

- Authors Ana Bokulić, Tajron Jurić, and Ivica Smolić address singularity resolution in black hole solutions using classical fields before quantum gravity
- Bronnikov's no-go theorems hinder the use of nonlinear electromagnetic fields for resolving singularities
- The authors propose Lagrangians incorporating both electromagnetic invariants $F_{ab}F^{ab}$ and $F_{ab}\,{\star F^{ab}}$
- Tension exists between a Lagrangian's Maxwellian weak field limit and boundedness of curvature invariants across theories
- Study highlights challenges and limitations in achieving singularity resolution through nonlinear electrodynamics, providing insights for future research

## Summary

In their paper titled "Constraints on singularity resolution by nonlinear electrodynamics," authors Ana Bokulić, Tajron Jurić, and Ivica Smolić address the longstanding issue of finding regular black hole solutions that resolve spacetime singularities using classical fields before delving into quantum gravity. The use of nonlinear electromagnetic fields for this purpose has been hindered by Bronnikov's no-go theorems, which focus on Lagrangians dependent solely on the electromagnetic invariant $F_{ab}F^{ab}$. Building upon Bronnikov's work, the authors consider Lagrangians that incorporate both electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F^{ab}}$. Through their research, they demonstrate that the tension between a Lagrangian's Maxwellian weak field limit and the boundedness of curvature invariants persists across a broader range of theories. This study sheds light on the challenges and limitations faced in achieving singularity resolution through nonlinear electrodynamics, offering valuable insights for future research in this field.