Related papers: Solving the characteristic initial value problem f…
We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy momentum tensor (EMT),…
We present the first numerical simulations of gravitational waves (GWs) passing through a potential well generated by a compact object in 3-D space, with a realistic source waveform derived from numerical relativity for the merger of two…
The (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations (GNNVEs) are investigated in order to search the influence of initial solution to exact solutions. The GNNVEs are converted into the combined equations of differently two…
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…
The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…
A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
An initial-boundary value problem for the $n$-dimensional wave equation is considered. A three-level explicit in time and conditionally stable 4th-order compact scheme constructed recently for $n=2$ and the square mesh is generalized to the…
The collision of two plane gravitational waves in Einstein's theory of relativity can be described mathematically by a Goursat problem for the hyperbolic Ernst equation in a triangular domain. We use the integrable structure of the Ernst…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation…
We consider interactions of exact (i.e., solutions of full nonlinear field equations) gravitational waves with matter by using the Einstein-Boltzmann equation. For a gravitational wave interacting with a system of massless particles, we…
To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are…
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional…
We construct a non-perturbative, single-valued solution for the metric and the motion of $N$ interacting particles in $2+1$-Gravity. The solution is explicit for two particles with any speed and for any number of particles with small speed.…
This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for…
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…