Construction of Regular Black Holes in General Relativity (1610.02636v3)

Abstract: We present a general procedure for constructing exact black hole solutions with electric or magnetic charges in General Relativity coupled to a nonlinear electrodynamics. We obtain a variety of two-parameter family spherically symmetric black hole solutions. In particular, the singularity at the central of the space-time can be cancelled in the parameters space and the black hole solutions become regular everywhere in the space-time. We study the global properties of the solutions and derive the first law of thermodynamics. We also generalize the procedure to include a cosmological constant and construct regular black hole solutions that are asymptotic to anti-de Sitter space-time.

• The paper introduces an analytical method that constructs exact regular black hole solutions by canceling central singularities via parameter degeneracies.
• It employs a nonlinear electrodynamics framework to parameterize mass and charge distributions, recovering models like Bardeen and Hayward.
• Derived thermodynamic properties, including the first law and Smarr relation, extend the solutions to both asymptotically flat and AdS space-times.

Overview of Regular Black Holes in General Relativity with Nonlinear Electrodynamics

The paper authored by Zhong-Ying Fan and Xiaobao Wang presents an analytical approach for constructing exact black hole solutions within the framework of General Relativity coupled with nonlinear electrodynamics. The authors focus on addressing the central singularity of black holes, proposing methods to derive solutions that are regular throughout the space-time. The research extends to both asymptotically flat and anti-de Sitter (AdS) scenarios.

The authors provide a comprehensive procedure for constructing black holes with either magnetic or electric charges via nonlinear electrodynamics. The solutions are demonstrated as part of a two-parameter family, with specific emphasis on the possibility of avoiding central singularities through parameter degeneracies. The method involves parameterizing the mass and charge distributions to cancel the space-time singularity at the origin.

Key Findings

1. Nonlinear Electrodynamics Framework:
   • The paper employs a Lagrangian density dependent on the electromagnetic invariant $\mathcal{F} = F_{\mu\nu}F^{\mu\nu}$. This approach allows for greater flexibility in modeling electromagnetic fields compared to linear electrodynamics.
2. Construction of Regular Black Holes:
   • By strategically setting the integration constants, the authors construct spherically symmetric black holes that are regular in space-time. Notably, they recover existing models like the Bardeen and Hayward black holes, which are characterized by regularity conditions and specific parameter values.
3. Thermodynamics and Energy Conditions:
   • The paper explores the global properties of these black holes, deriving the associated first law of thermodynamics alongside the Smarr relation. Additionally, it presents entropy product formulae for solutions with varying numbers of horizons.
   • The energy conditions, required for physical viability, differ across solutions. Regularity often comes with the violation of the strong energy condition, although some solutions preserve the weak energy condition.
4. Generalization to AdS Space:
   • The authors extend their method to include a cosmological constant, facilitating the construction of black holes in anti-de Sitter space-time with varying topologies. This work opens paths for applications in the AdS/CFT correspondence.

Implications

The paper enhances the repertoire of regular black hole solutions in the landscape of General Relativity coupled with nonlinear electrodynamics. By systematically avoiding singularities, these models offer potential insights into the quantum nature of gravity, bolstering theoretical models that purport non-singular black holes. Furthermore, the thermodynamic treatment adds layers of richness to the understanding of black hole thermodynamics, introducing new quantities and physical interpretations into the extended phase space.

Future Research Directions

This research paves the way for several future inquiries:

• Further exploration into the stability and dynamical aspects of these regular black hole solutions.
• Investigating the physical interpretations of new thermodynamic variables introduced by the nonlinear electrodynamics.
• Extending the framework to account for rotating black holes or more general charge configurations.
• Evaluating the implications for the information loss paradox and holographic duality in the context of AdS/CFT.

Through their work, Fan and Wang contribute significantly to the ongoing dialogue around the resolution of singularities in classical gravity and inspire future studies to build upon their innovative framework.