Related papers: Analytical external spherical solutions in entangl…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically…
We solve Einstein's constraint equations in the conformal thin-sandwich decomposition to model thin shells of non-interacting particles in circular orbit about a non-rotating black hole. We use these simple models to explore the effects of…
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
Classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordstr\"{o}m-Vlasov system is its relation to the…
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is…
We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of {\em weighted versions} of the classical integral operators associated with…
We derive a new interior solution for stellar compact objects in $f\mathcal{(R)}$ gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the…
We investigate the existence of static, spherically symmetric compact objects within the framework of symmetric teleparallel scalar-tensor gravity. This theory extends the Brans-Dicke and scalar-tensor models within the symmetric…
One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost…
We describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler, Thuburn, Klemp, and…
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action arising from trace dynamics. We give analytic and numerical results for the…