Related papers: Four-dimensional reflection groups and electrostat…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
An image system for a point charge outside a dielectric sphere is presented for all complex values of relative permittivity $\epsilon=\epsilon'+i\epsilon''$. The standard image integral solution of a point charge outside a dielectric sphere…
The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line,…
The method of image charges is a powerful and elegant technique in electrostatics, commonly used to determine the electric field generated by point charges near conductors of various shapes. While standard problems focus on single charges…
We point out that the moduli spaces of all known 3d $\mathcal{N}=$ 8 and $\mathcal{N}=$ 6 SCFTs, after suitable gaugings of finite symmetry groups, have the form $\mathbb{C}^{4r}/\Gamma$ where $\Gamma$ is a real or complex reflection group…
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative…
We show that in the grounded conducting sphere image problem, all the necessary information about the image charge can be found from a mirror equation and a magnification formula. Then, we propose a method to solve the image problem for an…
We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular…
The investigation of gravity in higher-dimensional spacetime has transitioned from a mathematical curiosity to a fundamental framework in theoretical physics, catalyzed by the dimensional requirements of String theory and M-theory. In this…
This is an investigation into the exact forms of images of point charges in 2D conducting ellipses and 3D prolate spheroids. For an ellipse with exterior point source, we compare two previous expressions for the analytic continuation inside…
We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times \Sigma$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $\Sigma$ is a sphere with two conical singularities known as a spindle. We…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We present a new infinite family of full spark frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously…
A one parameter family of static charged black hole solutions in $(2+1)$-dimensional general relativity minimally coupled to a dilaton $\phi\propto ln({r\over\beta})$ with a potential term $e^{b\phi}\Lambda$ is obtained. Their causal…
We present a set of noncommuting frame-translation symmetries in 4D gravity in tetrad-connection variables, which allow expressing diffeomorphisms as composite transformations. Working on the phase space level for finite regions, we pay…
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation…
A new approach to the analysis of the physical state space of a theory is presented within the general setting of local quantum physics. It also covers theories with long range forces, such as Quantum Electrodynamics. Making use of the…
In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labelled by their mass. We show that there are situations with many more black holes. We study…
We seek to obtain a new class of exact solutions of regular black holes in $f(T)$ Gravity with non-linear electrodynamics material content, with spherical symmetry in $4D$. The equations of motion provide the regaining of various solutions…
We consider static, spherically symmetric, electrically or/and magnetically charged configurations of a minimally coupled scalar field with an arbitrary potential $V(\phi)$ in general relativity. Using the inverse problem method, we obtain…