相关论文: RCCZ4: A Reference Metric Approach to Z4
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM…
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and…
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…
We study the convergence properties of our implementation of the 'moving punctures' approach at very high resolutions for an equal-mass, non-spinning, black-hole binary. We find convergence of the Hamiltonian constraint on the horizons and…
In this paper, we continue our investigations of R\'acz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which…
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…
The well-posedness of the gravitational equations of $f(R)$ gravity are studied in this paper. Three formulations of the $f(R)$ gravity with dynamical shifts (which are all based on the Arnowitt-Deser-Misner (ADM) formalism of the…
A Lagrangian density is provided, that allows to recover the Z4 evolution system from an action principle. The resulting system is then strongly hyperbolic when supplemented by gauge conditions like '1+log' or 'freezing shift', suitable for…
This paper studies Riemannian manifolds of the form $M \setminus S$, where $M^4$ is a complete four dimensional Riemannian manifold with finite volume whose metric is modeled on the complex hyperbolic plane $\mathbb{C} \mathbb{H}^2$, and…
The gauge polyvalence of a new numerical code is tested, both in harmonic-coordinate simulations (gauge-waves testbed) and in singularity-avoiding coordinates (simple Black-Hole simulations, either with or without shift). The code is built…
We consider two strongly hyperbolic Hamiltonian formulations of general relativity and their numerical integration with a free and a partially constrained symplectic integrator. In those formulations we use hyperbolic drivers for the shift…
We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We…
In this paper we consider the hyperbolic formulation of the constraints introduced by R\'acz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of…
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…
An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved…
$3+1$ formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is…
We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN…
Analog gravity systems have the unique opportunity to probe theoretical aspects of black hole physics in a controlled laboratory environment that one cannot easily observe for astrophysical black holes. In this work, we address the question…
The Rezzolla-Zhidenko (RZ) and Konoplya-Rezzolla-Zhidenko (KRZ) frameworks provide an efficient approach to characterize agnostically spherically symmetric or stationary black-hole spacetimes in arbitrary metric theories. In their original…
The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is…