Related papers: Nonlinear interaction of impulsive gravitational w…
In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations…
Impulsive gravitational waves are (weak) solutions to the Einstein vacuum equations such that the Riemann curvature tensor admits a delta singularity along a null hypersurface. The interaction of impulsive gravitational waves is then…
Consider the characteristic initial value problem for the Einstein vacuum equations without any symmetry assumptions. Impose a sequence of data on two intersecting null hypersurfaces, each of which is foliated by spacelike $2$-spheres.…
We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
When two non-interacting plane impulsive gravitational waves undergo a head-on collision, the vacuum interaction region between the waves after the collision contains backscattered gravitational radiation from both waves. The two systems of…
This is the second and last paper of a series aimed at solving the local Cauchy problem for polarized $\mathbb U(1)$ symmetric solutions to the Einstein vacuum equations featuring the nonlinear interaction of three small amplitude impulsive…
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…
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…
We study gravitational plane impulsive waves and electromagnetic shock waves in a scalar-tensor theory of gravity of the Brans-Dicke type. In vacuum, we present an exact solution of Brans-Dicke's field equations and give an example in which…
We present a space--time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the post collision space--time has…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in a…
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
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…
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus…