Related papers: Toward computing gravitational initial data withou…
Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the Spectral Einstein Code, to allow robust…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such…
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 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 new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null…
We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically…
A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of…
Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is described by an elliptic Poisson equation. We…
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…