Constructing hyperbolic systems in the Ashtekar formulation of general relativity (2008)
Hyperbolic formulation of equations of motion is an essential technique for proving well-posedness of the Cauchy problem of a system, and is also helpful for stable long time evolution in numerical...
Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity (2007)
Gen Yoneda Hisaaki, Gen Yoneda, Hisaaki Shinkai
We show how to treat the constraints and reality conditions in the SO(3)-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify...
Constraint propagation in N+1-dimensional space-time (2004)
Shinkai, Hisa-aki, Yoneda, Gen
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...
Shinkai, Hisa-aki, Yoneda, Gen
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...
Diagonalizability of Constraint Propagation Matrices (2002)
Yoneda, Gen, Shinkai, Hisa-aki
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...
Yoneda, Gen, Shinkai, Hisa-aki
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)....
Shinkai, Hisa-aki, Yoneda, Gen
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...
Constraint propagation in the family of ADM systems (2001)
Yoneda, Gen, Shinkai, Hisa-aki
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...
Shinkai, Hisa-aki, Yoneda, Gen
In order to perform accurate and stable long-term numerical integration of the Einstein equations, several hyperbolic systems have been proposed. We here report our numerical comparisons between...
In a previous paper (G.Yoneda, Proc.R.Soc.London, A445,(1994),221), we proved the no-interaction theorem for four particles with the assumption that the (linear and angular) momentum on space-like...
Yoneda, Gen, Shinkai, Hisa-aki
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...
Shinkai, Hisa-aki, Yoneda, Gen
In order to perform accurate and stable long-time numerical integration of the Einstein equation, several hyperbolic systems have been proposed. We here present numerical comparisons between weakly...
Asymptotically constrained and real-valued system based on Ashtekar's variables (1999)
Shinkai, Hisa-aki, Yoneda, Gen
We present a set of dynamical equations based on Ashtekar's extension of the Einstein equation. The system forces the space-time to evolve to the manifold that satisfies the constraint equations or...
Constructing hyperbolic systems in the Ashtekar formulation of general relativity (1999)
Yoneda, Gen, Shinkai, Hisa-aki
Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time...
Symmetric hyperbolic system in the Ashtekar formulation (1998)
Yoneda, Gen, Shinkai, Hisa-aki
We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with...
Lorentzian dynamics in the Ashtekar gravity (1997)
Shinkai, Hisa-aki, Yoneda, Gen
We examine the advantages of the SO(3)-ADM (Ashtekar) formulation of general relativity, from the point of following the dynamics of the Lorentzian spacetime in direction of applying this into...
A trick for passing degenerate points in Ashtekar formulation (1997)
Yoneda, Gen, Shinkai, Hisaaki, Nakamichi, Akika
We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming...
Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity (1996)
We show how to treat the constraints and reality conditions in the $SO(3)$-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We...