Nonlinear electrodynamics as a symmetric hyperbolic system

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg

Light propagation in (2+1)-dimensional electrodynamics: the case of nonlinear constitutive laws

We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in $2+1$-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the polarization of waves are derived and three special cases are analyzed in details. In spite of the dimensional reduction, our model still presents phenomena like one-way propagation, controlled opacity among others for a large class of dielectric and magneto-electric parameters.Comment: 9 pages, 7 figure

A classification of the effective metric in nonlinear electrodynamics

We show that only two types of effective metrics are possible in certain nonlinear electromagnetic theories. This is achieved by using the dependence of the effective metric on the energy-momentum tensor of the background along with the Segr\`e classification of the latter. Each of these forms is completely determined by single scalar function, which characterizes the light cone of the nonlinear theory. We compare this light cone with that of Minkowski in two examples.Comment: Accepted for publication in Classical & Quantum Gravit

Malignant lung PEComa (clear cell tumor): rare case report and literature review

Clear cell tumors of the lung (CCTL), or “sugar tumors” of lung, are very uncommon lesions and are mostly benign perivascular epithelioid cell (PEC) tumors with no specific morphologic features. Fewer than 100 cases have been reported; the aggressive nature demonstrated in sporadic reports has rarely been described in the literature. Although the course is generally described as benign, eight reported cases showed malignant behavior. We report a case of a PEC with a malignant presentation in a young man, correlating the main characteristics of the tumor with other cases reported in the literature to better elucidate this rare presentation. We also performed a literature review of reports on benign and malignant CCTL cases, with a focus on clinical, imaging, and immunohistochemical differentiation. CCTLs are rare tumors that require histopathological and immunohistochemical confirmation; to date, criteria that can predict malignant evolution are lacking

From disformal electrodynamics to exotic spacetime singularities

We study different types of spacetime singularities which emerge in the context of disformal electrodynamics. The latter is characterized by transformations of the background metric which preserve regular (non-null) solutions of Maxwell equations in vacuum. Restricting ourselves to the case of electrostatic fields created by charged point particles along a line, we show that exotic types of singularities arise.Comment: 18 pages, 4 figure