AdS--dS Stationary Rotating Black Hole Exact Solution within Einstein--Nonlinear Electrodynamics

• Published in: arXiv.org
• Main Author: García Díaz, Alberto A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 26.01.2022
• Subjects: Black holes; Cosmological constant; Eigenvalues; Electrodynamics; Event horizon; Exact solutions; Mathematical analysis; Parameters; Physics - General Relativity and Quantum Cosmology; Rotation; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2201.10682

In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant \(\Lambda\), and three parameters due to the nonlinear electrodynamics: \(\beta\) is associated to the potential vectors \(A_\mu\) and \({}^{\star}P_\mu\), and two constants, \(F_0\) and \(G_0\), due to the presence of the invariants \(F\) and \(G\) in the Lagrangian \(L(F(\,x^{\mu}),G(\,x^{\mu}))\). This solution is of Petrov type D, characterized by the Weyl tensor eigenvalue \(\Psi_2\), the traceless Ricci tensor eigenvalue \(S=2\Phi_{(11)}\), and the scalar curvature \(R\); it allows for event horizons, exhibits a ring singularity and fulfils the energy conditions. Its Maxwell limit is the de Sitter-Anti--de Sitter--Kerr--Newman black hole solution.