Related papers: Formulations of the Einstein equations for numeric…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in…
The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here…
Several numerical relativity groups are using a modified ADM formulation for their simulations, which was developed by Nakamura et al (and widely cited as Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown…
With a purpose of constructing a robust evolution system against numerical instability for integrating the Einstein equations, we propose a new formulation by adjusting the ADM evolution equations with constraints. We apply an adjusting…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
We present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM…
Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for…
Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the…
We present our numerical comparisons between the BSSN formulation widely used in numerical relativity today and its adjusted versions using constraints. We performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests, proposed by…
In order to obtain stable and accurate general relativistic simulations, re-formulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for…
Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…
In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura (BSSN) equations.The idea is to add functional…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the ADM…
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…
A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST system…
We introduce a set of constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing…