Related papers: On boundary conditions for linearised Einstein's e…
We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of…
This article is devoted to the numerical study of the existence of the eigenvalues of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ in the presence of an electric field of constant…
We will study solvability of nonlinear second-order elliptic system of partial differential equations with nonlinear boundary conditions. We study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the…
We analyze the propagation and polarization properties of high-frequency gravitational waves in Einstein-\AE ther theory on vorticity-free and slowly-varying backgrounds at both leading and next-to-leading orders within the geometric optics…
This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
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…
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…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
We deal with rigidity results for compact gradient Einstein-type manifolds with nonempty boundaries. As a result, we obtain new characterizations for hemispheres and geodesic balls in simply connected space forms. In dimensions three and…
Novel applications of Numerical Relativity demand for more flexible algorithms and tools. In this paper, I develop and test a multigrid solver, based on the infrastructure provided by the Einstein Toolkit, for elliptic partial differential…
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field…
In this paper, we will provide a result on the relativistic Euler equations for an ideal gas equation of state and a physical vacuum boundary. More specifically, we will prove a priori estimates for the linearized system in weighted Sobolev…
A theoretical description of electromagnetic waves in the background of a (weak) gravitational wave is presented. Explicit expressions are obtained for the Stokes parameters during the passage of a plane-fronted gravitational wave described…
We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of…
We prove regularity results up to the boundary for time independent generalized Maxwell equations on Riemannian manifolds with boundary using the calculus of alternating differential forms. We discuss homogeneous and inhomogeneous boundary…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…