Related papers: Hyperboloidal data and evolution
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
We study the evolution of nonlinear superhorizon perturbations in a universe dominated by a complex scalar field. The analysis is performed adopting the gradient expansion approach, in the constant mean curvature slicing. We derive general…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
The behaviour of the Maxwell field near one of the spatial infinities of the Schwarzschild solution is analysed by means of the transport equations implied by the Maxwell equations on the cylinder at spatial infinity. Initial data for the…
We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity.…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
Numerical relativity simulations provide a means by which to study the evolution and end point of strong over-densities in cosmological spacetimes. Specific applications include studies of primordial black hole formation and the robustness…
Cosmic strings are topological defects thought to have formed early in the life of the universe. If such objects exist, a study of their interaction with black holes is of interest. The equations of motion of a cosmic string have the form…
We use the Kerr-Schild type Teukolsky equation (horizon penetrating) to evolve binary black hole initial data as proposed by Bishop {\em et al.} in the close limit. Our results are in agreement with those recently obtained by Sarbach {\em…
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the…
Gravitational collapse and bubble evolution in the asymptotical Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze dynamics for contact \sch-FLRW (McVittie) spacetimes,…
We develop a variational approach in order to study the qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss long-time behavior, invariance properties, and ultracontractivity of…
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…
Nonspherical perturbation theory has been necessary to understand the meaning of radiation in spacetimes generated through fully nonlinear numerical relativity. Recently, perturbation techniques have been found to be successful for the time…
Regge calculus is used to construct initial data for vacuum axisymmetric Brill waves at a moment of time symmetry. We argue that only a tetrahedral lattice can successfully reproduce the continuum solution, and develop a simplicial…
Motivated by the need of a robust geometrical framework for the calculation of long, and highly accurate waveforms for extreme-mass-ratio inspirals, this work presents an extensive study of the hyperboloidal formalism for the Kerr spacetime…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…
We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the…
We study the formation of primordial black holes and the generation of gravitational waves in a class of cosmological models that are direct supersymmetric analogs of the observationally favored nonminimally coupled Higgs inflation model.…
In this paper, the Eddington-Finkelstein transformation is used as an illustration of how the problem of singularities or infinities can be removed by application of nonstandard analysis to the Schwarzschild line element (metric). The…