Received: 3 June 2024 / Accepted: 10 July 2024 / Published online: 26 July 2024 | G. Alencar, Kirill A. Bronnikov, Manuel E. Rodrigues, Diego Sáez-Chillón Gómez, Marcos V. de S. Silva
This paper explores the construction of regular black hole and wormhole solutions in the framework of non-linear electrodynamics (NED) with a scalar field. The authors implement a reconstruction method to show that such solutions can be accommodated in NED, particularly focusing on electrically charged sources of matter. The paper covers both spherically symmetric and cylindrically symmetric black bounces (BB) in 3+1 dimensions and regular black strings in 2+1 dimensions. Key findings include:
1. **Spherically Symmetric BB Solutions**: The authors reconstruct the Lagrangian for NED and the scalar field potential for various BB solutions, including the Simpson-Visser and Bardeen black bounces. These solutions are shown to be consistent with electric sources, unlike previous studies that used magnetic sources.
2. **Cylindrically Symmetric BB Solutions**: Two specific examples of cylindrical black strings are analyzed, demonstrating the reconstruction of the NED Lagrangian and scalar field potential. The dependence of the electromagnetic invariant \( F \) on the scalar field \( \phi \) is discussed, highlighting the non-monotonic relationship between \( F \) and \( P \), which leads to different branches of the Lagrangian function \( L(F) \).
3. **2+1 Dimensional BB Solutions**: The paper also explores regular black hole solutions in 2+1 dimensions, such as the regular BTZ black hole and the Einstein-CIM space-time. These solutions are shown to violate classical energy conditions, including the Null Energy Condition (NEC).
4. **Energy Conditions**: The authors analyze the Null Energy Condition (NEC) for all the discussed solutions, showing that they violate this condition, which implies violations of the weak, strong, and dominant energy conditions.
The paper concludes by discussing the importance of understanding the sources of BB and other regular space-times for various physical phenomena, such as thermodynamics, shadows, and causality. The authors suggest further research into the viability of the considered Lagrangians and the extension of these solutions to more realistic theoretical models.This paper explores the construction of regular black hole and wormhole solutions in the framework of non-linear electrodynamics (NED) with a scalar field. The authors implement a reconstruction method to show that such solutions can be accommodated in NED, particularly focusing on electrically charged sources of matter. The paper covers both spherically symmetric and cylindrically symmetric black bounces (BB) in 3+1 dimensions and regular black strings in 2+1 dimensions. Key findings include:
1. **Spherically Symmetric BB Solutions**: The authors reconstruct the Lagrangian for NED and the scalar field potential for various BB solutions, including the Simpson-Visser and Bardeen black bounces. These solutions are shown to be consistent with electric sources, unlike previous studies that used magnetic sources.
2. **Cylindrically Symmetric BB Solutions**: Two specific examples of cylindrical black strings are analyzed, demonstrating the reconstruction of the NED Lagrangian and scalar field potential. The dependence of the electromagnetic invariant \( F \) on the scalar field \( \phi \) is discussed, highlighting the non-monotonic relationship between \( F \) and \( P \), which leads to different branches of the Lagrangian function \( L(F) \).
3. **2+1 Dimensional BB Solutions**: The paper also explores regular black hole solutions in 2+1 dimensions, such as the regular BTZ black hole and the Einstein-CIM space-time. These solutions are shown to violate classical energy conditions, including the Null Energy Condition (NEC).
4. **Energy Conditions**: The authors analyze the Null Energy Condition (NEC) for all the discussed solutions, showing that they violate this condition, which implies violations of the weak, strong, and dominant energy conditions.
The paper concludes by discussing the importance of understanding the sources of BB and other regular space-times for various physical phenomena, such as thermodynamics, shadows, and causality. The authors suggest further research into the viability of the considered Lagrangians and the extension of these solutions to more realistic theoretical models.