Related papers: Characteristic Evolution and Matching
The characteristic initial value problem has been implemented as a robust computational algorithm (the PITT NULL CODE), with direct application to binary black holes. The event horizon can be analyzed by characteristic techniques as a…
Computational methods are essential to provide waveforms from coalescing black holes, which are expected to produce strong signals for the gravitational wave observatories being developed. Although partial simulations of the coalescence…
We investigate some regularity properties of a class of doubly nonlinear anisotropic evolution equations whose model case is \begin{align*} \partial_t \big(|u|^{\alpha -1}u \big) - \sum^N_{i=1} \partial_i \big( |\partial_i u|^{p_i - 2}…
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…
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
We describe the first axisymmetric numerical code based on the generalized harmonic formulation of the Einstein equations which is regular at the axis. We test the code by investigating gravitational collapse of distributions of complex…
Existence of strong solutions of an abstract Cauchy problem for a class of doubly nonlinear evolution inclusion of second order is established via a semi-implicit time discretization method. The principal parts of the operators acting on…
This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…
The evolution of black holes in "confining boxes" is interesting for a number of reasons, particularly because it mimics the global structure of Anti-de Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy problem…
This paper deals with the following Cauchy problem to nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness $$ \left\{\begin{array}{ll} ^CD^{\alpha}_tu(t)+A(t)u(t)=…
We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures.…
The most general bound binary black hole (BBH) system has an eccentric orbit and precessing spins. The detection of such a system with significant eccentricity close to the merger would be a clear signature of dynamical formation. In order…
We study the Cauchy problem for the radial energy critical nonlinear wave equation in three dimensions. Our main result proves almost sure scattering for radial initial data below the energy space. In order to preserve the spherical…
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gowdy space-times. The simple objective of this paper is to…
We have developed a new numerical code to study the evolution of distorted, rotating black holes. We discuss the numerical methods and gauge conditions we developed to evolve such spacetimes. The code has been put through a series of tests,…
During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…