Related papers: The initial value problem in numerical relativity
I describe the conformal method for constructing solutions of the hyperboloidal constraint equations as well as the conditions needed on the free data in order to have regularity up to boundary for the solutions to the constraint equations.…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
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…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic…
We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable…
Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying…
We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily…
We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…
We discuss the implementation, to the case of compact manifolds, of the perturbative method of Friedrich-Butscher for the construction of solutions to the vaccum Einstein constraint equations. This method is of a perturbative nature and…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
The conformal method developed in the 1970s and the more recent Lagrangian and Hamiltonian conformal thin-sandwich methods are techniques for finding solutions of the Einstein constraint equations. We show that they are manifestations of a…
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…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…