Related papers: Improved outer boundary conditions for Einstein's …
Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…
We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
We consider an exterior electromagnetic field surrounding a rotating star endowed with a dipole magnetic field in the context of general relativity. The analytic solution for a stationary configuration is obtained, and the general…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-AdS system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
We present an exact electrovacuum solution of Einstein-Maxwell equations with infinite sets of multipole moments which can be used to describe the exterior gravitational field of a rotating charged mass distribution. We show that in the…
We consider fully nonlinear obstacle-type problems of the form \begin{equation*} \begin{cases} F(D^{2}u,x)=f(x) & \text{a.e. in}B_{1}\cap\Omega,|D^{2}u|\le K & \text{a.e. in}B_{1}\backslash\Omega, \end{cases} \end{equation*} where $\Omega$…
We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error…
We investigate the semiclassical approach to the lensing of photons in a spherically symmetric gravitational background, starting from Born level and include in our analysis the radiative corrections obtained from the electroweak theory for…
Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
Absorbing boundary condition approach to nuclear breakup reactions is investigated. A key ingredient of the method is an absorbing potential outside the physical area, which simulates the outgoing boundary condition for scattered waves.…