(2+1)(2+1)-dimensional regular black holes with nonlinear electrodynamics sources

On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of $(2+1)$-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct $(2+1)$-dimensional regular black holes. In this manner, we construct four $(2+1)$-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes and verify the first law of black hole thermodynamics.Comment: 13 pages, 4 figures. in press in PL

An omnidirectional retroreflector based on the transmutation of dielectric singularities

In the field of transformation optics, metamaterials mimic the effect of coordinate transformations on electromagnetic waves, creating the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here we report the achievement of another "impossible task". We implement, for microwaves, a device that would normally require a dielectric singularity, an infinity in the refractive index. We transmute a singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility, from all directions. Our method is robust, potentially broadband and similar techniques could be applied for visible light