Generic Behavior of Electromagnetic Fields of Regular Rotating Electrically Charged Compact Objects in Nonlinear Electrodynamics Minimally Coupled to Gravity

Abstract

Regular rotating electrically charged compact objects are described by nonlinear electrodynamics minimally coupled to gravity in a self-consistent way and without additional assumptions on the relation between the electromagnetic field and gravity. The electromagnetic fields obey the system of four source-free nonlinear equations for the electromagnetic tensor Fμν, with only two independent components due to spacetime symmetry determined by the algebraic structure of electromagnetic stress–energy tensors (pr=−ρ). In this paper, we present, for an arbitrary gauge-invariant Lagrangian, the general regular solution and generic behavior of electromagnetic fields, including the generic features of the Lagrange dynamics, for regular rotating electrically charged black holes and electromagnetic spinning solitons.

Density and Mass Function for Regular Rotating Electrically Charged Compact Objects Determined by Nonlinear Electrodynamics Minimally Coupled to Gravity

“…General solutions for two independent field components have been found in our recent paper [71]. The aim of this paper is to show that NED-GR determines uniquely the electromagnetic density ρ(r) and the mass function M(r), and to obtain the electromagnetic density and mass function from the compatibility condition.…”

“…Violation of WEC in (20) would involve the negative values of the dielectric and magnetic permeability, which is incompatible with the basic requirements of electrodynamics of continuous media [75]). Therefore the NED-GR electrically charged objects always satisfy WEC [71].…”

“…where L is the Lagrangian, and L F is its derivative, L F = dL/dF. The condition ( 6) is not satisfied in the axially symmetric geometry where [71] 8πT…”

“…The electromagnetic density and pressures obtained as the eigenvalues of the electromagnetic stress-energy tensor ( 14) are given by [71] 8πρ…”

“…In nonlinear electrodynamics, minimally coupled to gravity, the electromagnetic field of regular rotating electrically charged objects is described by four dynamical equations for two independent components of the electromagnetic tensor F µν , restricted by the necessary and sufficient condition of their compatibility, imposed on the Lagrange derivative L F = dLdF, and by two constraints imposed on the integration functions in general solutions [71]. As a result, three independent dynamical equations uniquely define three basic field functions: two independent components of F µν and the Lagrange derivative L F , which is directly related with the spherical electromagnetic density ρ(r) and the mass function M(r).…”