Researchers H. Babaei-Aghbolagh, Komeil Babaei Velni, Song He, and Fateme Isapour, affiliated with various institutions including the University of Tehran and Sharif University of Technology, have recently published a study that delves into the complex interplay between gravity and electromagnetism in the context of black hole physics. Their work, titled “A Unified Causal Framework for Nonlinear Electrodynamics Black Hole from Courant-Hilbert Approach: Thermodynamics and Singularity,” was published in the journal Physical Review D.
The team has developed a comprehensive framework to analyze the thermodynamics and structure of black holes in anti-de Sitter (AdS) backgrounds, focusing on Einstein gravity coupled with nonlinear electrodynamics (NED). The electromagnetic sector of their model is governed by a Generalized Nonlinear Electrodynamics (GNED) Lagrangian, which is constructed using the Courant-Hilbert approach. This ensures that the theory maintains duality invariance and causal propagation, encompassing various well-known models such as ModMax, Generalized Born-Infeld (GBI), and self-dual logarithmic electrodynamics as continuous limits.
Within this unified framework, the researchers obtained exact solutions for charged AdS black holes and conducted a thorough examination of their thermodynamic properties. They found that the phase structure of these black holes exhibits van der Waals-type transitions between small and large black holes, characterized by a swallowtail in the free energy at the critical point. This behavior is reminiscent of phase transitions observed in classical thermodynamics and provides insights into the complex behavior of black hole systems.
The study also investigates the internal geometry of these black holes, demonstrating how the nature of the central singularity is influenced by the matter fields sourcing the spacetime. By analyzing the Kretschmann scalar, the researchers showed that gravity and electromagnetism jointly control the curvature blow-up in charged and ModMax black holes, with gravity being the dominant factor. In contrast, the GBI and logarithmic NED models exhibit distinct singularity profiles that are governed by the specific functional forms of their Lagrangians.
The near-origin behavior of the metric was also examined to identify the parameter ranges that support an event horizon and to determine when the solution instead becomes a naked singularity. The comparison across different causal NED theories revealed that each model produces identifiable signatures in both the strength of the singularity and the conditions for horizon formation.
While this research is primarily theoretical and focuses on fundamental aspects of black hole physics, it has potential implications for the energy sector, particularly in the context of advanced energy technologies and theoretical models that could inspire innovative approaches to energy generation and management. The study’s insights into the behavior of complex systems under extreme conditions could contribute to the development of more robust and efficient energy solutions.
This article is based on research available at arXiv.