Related papers: Constraint-preserving Sommerfeld conditions for th…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
We derive the Helmholtz--Korteweg equation, which models acoustic waves in Korteweg fluids. We further derive a nematic variant of the Helmholtz-Korteweg equation, which incorporates an additional orientational term in the stress tensor.…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
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…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
We present new many-parameter families of strongly and symmetric hyperbolic formulations of Einstein's equations that include quite general algebraic and live gauge conditions for the lapse. The first system that we present has 30 variables…
The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint…
In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays at a rate $\tau^{-2+}$ for the solution of the linearized…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
Second-order tensor perturbations induced by primordial fluctuations play a crucial role in probing small-scale physics, but gauge dependence of their energy density has remained a fundamental challenge in cosmological perturbation theory.…
We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose - Einstein…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
Electrodynamics in curved spacetime can be studied in the Eastwood--Singer gauge, which has the advantage of respecting the invariance under conformal rescalings of the Maxwell equations. Such a construction is here studied in Einstein…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…