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In the present paper we study the singularity structure of the exterior field of neutron stars with the aid of the four-parameter exact solution of the Einstein-Maxwell equations. The complete analysis of this problem in the generic case becomes possible due to the implementation of the novel analytical approach to the resolution of the singularity condition, and it shows the absence of the ring singularities off the symmetry axis in the positive mass case, as well as the possibility of the removal of the ring singularity by a strong magnetic field in the negative mass case. The solution takes an extraordinarily simple form in the equatorial plane, very similar to that of the Kerr solution, which makes it most suitable for astrophysical applications as the simplest model of a rotating magnetized deformed mass. It also provides a nontrivial example confirming a recent claim that the $\varphi$ component of the electromagnetic four-potential has features inconsistent with the intrinsic properties of the electrovac metric, while the magnetic field is represented correctly by the $t$ component of the dual electromagnetic four-potential., Comment: 21 pages, no figures

Given a compact Riemann surface $X$ of genus at least $2$ with automorphism group $G$ we provide formulae that enable us to compute traces of automorphisms of X on the space of global sections of $G$-linearized line bundles defined on certain blow-ups of proyective spaces along the curve $X$. The method is an adaptation of one used by Thaddeus to compute the dimensions of those spaces. In particular we can compute the traces of automorphisms of $X$ on the Verlinde spaces corresponding to the moduli space $SU_{X}(2,\xi)$ when $\xi$ is a line bundle $G$-linearized of suitable degree., Comment: 48 pages

Stationary axisymmetric metric describing the exterior field of a rotating, charged sphere endowed with magnetic dipole moment is presented and discussed. It has a remarkably simple multipole structure defined by only four nonzero Hoenselaers-Perj\'es relativistic moments., Comment: 6 pages, no figures; a minor misprint in formulas (13) rectified

In the present paper we argue that a special case of the Bach-Weyl metric describing a static configuration of two Schwarzschild black holes gives rise, after extending its parameter space to complex values, to a very simple 2-parameter model for the gravitational field of a static deformed mass. We compare this model, which has no restrictions on the quadrupole parameter, with the well-known Zipoy-Voorhees $\delta$-metric and show in particular that the mass quadrupole moment in the latter solution cannot take arbitrary negative values. We subsequently add an arbitrary angular momentum to our static model and study some properties of the resulting 3-parameter stationary solitonic spacetime, which permits us to introduce the notion of the Fodor-Hoenselaers-Perj\'es relativistic multipole moments., Comment: 17 pages, no figures, typos in formulas (24) fixed

Thin Film technology has widespread applications in everyday electronics, notably Liquid Crystal Display screens, solar cells, and organic light emitting diodes. We explore the potential of this technology as charged particle radiation tracking detectors for use in High Energy Physics experiments such as those at the Large Hadron Collider or the Relativistic Heavy Ion Collider. Through modern fabrication techniques, a host of semiconductor materials are available to construct thin, flexible detectors with integrated electronics with pixel sizes on the order of a few microns. We review the material properties of promising candidates, discuss the potential benefits and challenges associated with this technology, and review previously demonstrated applicability as a neutron detector., Comment: 9 pages, 3 figures, 3 tables

The aim is to give a geometric characterization of the finite generation of the Cox ring of anticanonical rational surfaces. This characterization is encoded in the finite generation of the effective monoid. Furthermore, we prove that in the case of a smooth projective rational surface having a negative multiple of its canonical divisor with only two linearly independent global sections (e.g., an elliptic rational surface), the finite generation is equivalent to the fact that there are only a finite number of smooth projective rational curves of self-intersection -1. The ground field is assumed to be algebraically closed of arbitrary characteristic.