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The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
The new solution of the Einstein equations in empty space is presented. The solution is constructed using Schwarzschild solution but essentially differs from it. The basic properties of the solution are: the existence of a horizon which is…
We prove global existence for Einstein's equations with a charged scalar field for initial conditions sufficiently close to the Minkowski spacetime without matter. The proof relies on generalized wave coordinates adapted to the outgoing…
We study the nonlinear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of cosmological black holes, we construct the solution of the…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein…
The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We…
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1…
Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity . This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are…
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our…