Related papers: Numerical treatment of the hyperboloidal initial v…
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…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
Some issues in the numerical treatment of the conformal field equations are discussed. In particular, the problem of obtaining smooth initial data for the hyperboloidal initial value problem is described and solution methods are presented.
A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical…
The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
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…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
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 present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a…