Related papers: Characteristic Evolution and Matching
We present a new approach for the Cauchy-characteristic extraction of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic…
In general Evolutionary Computation (EC) includes a number of optimization methods inspired by biological mechanisms of evolution. The methods catalogued in this area use the Darwinian principles of life evolution to produce algorithms that…
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 formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
We develop a relativistic framework to investigate the evolution of cosmological structures from the initial density perturbations to the highly nonlinear regime. Our approach involves proposing a procedure to match ``best-fit", exact…
The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via…
We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the…
We take further steps in the development of the characteristic approach to enable handling the physical problem of a compact self-gravitating object, such as a neutron star, in close orbit around a black hole. We examine different options…
We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional…
Over the past 30 years many researchers in the field of evolutionary computation have put a lot of effort to introduce various approaches for solving hard problems. Most of these problems have been inspired by major industries so that…
This study explores the impact of cosmic curvature on structure formation through general relativistic first-order perturbation theory. We analyze continuity and Euler equations, incorporating cosmic curvature into Einstein equations.…
We derive an exact analytical solution for the redshift evolution of linear and scale-independent bias, by solving a second order differential equation based on linear perturbation theory. This bias evolution model is applicable to all…
We study the generation of singularities from the initial datum for a solution of the Cauchy problem for a class of Hamilton-Jacobi equations of evolution. For such equations, we give conditions for the existence of singular generalized…
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.…
We consider a class of partial differential equations with Carlitz derivatives over a local field of positive characteristic, for which an analog of the Cauchy problem is well-posed. Equations of such type correspond to quasi-holonomic…