A note on Reissner–Nordström black holes in the inverse electrodynamics model

Recently, the inverse electrodynamics model (IEM) was introduced and applied to find Reissner–Nordström black holes in the context of the general relativity coupled minimally with the nonlinear electrodynamics. The solution consists of both electric and magnetic fields as of the dyonic solutions. Here, in this note, we show that the IEM model belongs to a more general class of the nonlinear electrodynamics with [Formula: see text]. Here, [Formula: see text] is the energy momentum tensor of the nonlinear electrodynamic Lagrangian. Naturally, such a dyonic RN black hole solution is the solution for this general class.

Exact black hole solutions with nonlinear electrodynamic field

We construct exact black hole solutions to Einstein gravity with nonlinear electrodynamic field. In these solutions, there are, in general, four parameters. They are physical mass, electric charge, cosmological constant and the coupling constant. These solutions differ significantly from the Reissner–Nordström–de Sitter solution in Einstein–Maxwell gravity with a cosmological constant, due to the presence of coupling constant. For example, some of them are endowed with a topological defect on angle [Formula: see text] and the electric charge of some can be much larger or smaller than their mass by varying the coupling constant. On the other hand, these spacetimes are all asymptotically de Sitter (or anti-de Sitter). As a result, their causal structure is similar to the Reissner–Nordström–de Sitter spacetime. Finally, the investigations on the thermodynamics reveal that the coupling constant except for solution-4 has the opposite effect as temperature on the phase, structure of black holes. Concretely, the phase-space changes from single phase to three phases with the decrease of temperature. On the contrary, it changes from three phases to a single phase with the decrease of coupling constant.

(2 + 1)-dimensional dynamical black holes in Einstein-nonlinear Maxwell theory

Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born–Infeld electrodynamics.

Surface Impedance Boundary Conditions applied to solving nonlinear electrodynamic systems

The paper presents a method for solving electromagnetic field problems by applying impedance boundary conditions for systems including conducting bodies of nonlinear magnetic properties in an excited harmonic field. Three types of impedance boundary conditions were derived. A procedure for computing surface impedance based on the transfer matrix is proposed. This procedure has been tested by comparing computational results to calculations where time function distortions were considered, and to the experimental data.