We present a set of lecture notes for modeling stellar structure in regimes where general relativistic effects become important, such as for neutron stars. The framework draws directly from solving the Einstein equation for a spherically symmetric star in static equilibrium in terms of energy density, pressure, and a term like the gravitational potential. The equation is presented as a somewhat...

Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in [1], we prove without any additional prerequisite conditions that the solution of the Wigner equation with symmetric potential and inflow boundary conditions will be symmetric. This improve the result in [6] which depends on the convergence of solution formulated in the Neumann series. By nume...

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a nite di erences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtai...

We find the general solution of the Einstein equation for spherically symmetric collapse of Type II fluid (null strange quark fluid) in higher dimensions. It turns out that the nakedness and curvature strength of the shell focusing singularities carry over to higher dimensions. However, there is shrinkage of the initial data space for a naked singularity of the Vaidya collapse due to the presen...

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (diver...

PT-symmetric solutions of Schrödinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials ar...

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform converg...

The spherically symmetric thin shells of the quark-gluon plasma are considered within the framework of general relativity and bag model. The equation of state for two-dimensional plasma is suggested, and its features are discussed. The exact equations of motion of the quark-gluon plasma shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the condit...

In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions of gravitational field equation. The “spin” angular momentum, the energy-momentum and the “extended orbital angular momentum” are explicitly given for each s...