Black Hole Solutions with Electric and Magnetic Charges in Nonlinear Electrodynamic

Abstract

This review article provides a comprehensive and self-contained overview of black hole solutions coupled to nonlinear electrodynamics (NLED) with both electric and magnetic charges. We systematically discuss the theoretical foundations, including the general action principle, the Hamiltonian P-framework for constructing exact solutions, and the classification of NLED theories (Born-Infeld, Euler-Heisenberg, power-law, logarithmic, exponential, and regular models). Detailed derivations are presented for dyonic black hole solutions in each theory, including explicit metric functions, asymptotic expansions, and horizon structures. The thermodynamic properties are examined in depth, including the first law, Smarr relations, heat capacities, extended phase space thermodynamics with p-V criticality, and the effect of magnetic charge on phase transitions. The geodesic structure is analyzed with complete calculations of null and timelike geodesics, photon spheres, black hole shadows, and gravitational lensing. Regular black hole solutions that resolve the central singularity are discussed with detailed analysis of energy conditions. Holographic applications via the AdS/CFT correspondence are explored, including holographic superconductors, entanglement entropy, and conductivity. Connections to quantum gravity through the weak gravity conjecture, swampland criteria, and string theory embeddings are examined.

35 pages