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The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
We study odd dimensional charged equally rotating black holes in the Einstein-Maxwell theory with/without a cosmological constant by using the large D expansion method, where D is a spacetime dimension. Solving the Einstein-Maxwell…
We study the thermodynamical properties of electrically charged black hole solutions of a nonlinear electrodynamics theory defined by a power p of the Maxwell invariant, which is coupled to Einstein gravity in four and higher spacetime…
It is shown that the Born--Infeld nonlinear electrodynamics with a polynomial type nonlinearity accommodates finite-energy electric point charges but rejects finite-energy magnetic point charges, or monopoles, thereby spelling out an…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
Using a nonlinear electrodynamics coupled to teleparallel theory of gravity, three regular charged spherically symmetric solutions are obtained. The nonlinear theory reduces to the Maxwell one in the weak limit and the solutions correspond…
In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal…
Modified Maxwell electrodynamics, or ModMax for short, is the unique nonlinear extension of Maxwell's theory that preserves its notable symmetries: conformal invariance and electromagnetic duality. ModMax has been studied extensively at the…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We…
The nonlinear Maxwell Lagrangian preserving both conformal and SO(2) duality-rotation invariance has been introduced very recently. Here, in the context of Einstein's theory of gravity minimally coupled with this nonlinear electrodynamics,…
We discuss a new analytic solution to the Einstein-Maxwell field equations that describes electrically charged black holes with a slow rotation and with a single angular momentum in all higher dimensions. We also compute the gyromagnetic…
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a negative…
A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from…
A natural modification of the equations of covariantly-constant vector fields (CCVF) in Weyl geometry leads us to consider a metric compatible geometry possessing conformal curvature and torsion fully determined by its trace. The latter is…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…