33 research outputs found
Constraint propagation in N+1-dimensional space-time
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 future numerical research of higher-dimensional space-time, we
study the dimensional dependence of constraint propagation behavior. The
Arnowitt-Deser-Misner evolution equation has matter terms which depend on ,
but the constraints and constraint propagation equations remain the same. This
indicates that there would be problems with accuracy and stability when we
directly apply the ADM formulation to numerical simulations as we have
experienced in four-dimensional cases. However, we also conclude that previous
efforts in re-formulating the Einstein equations can be applied if they are
based on constraint propagation analysis.Comment: 4 pages, to appear in Gen. Rel. Gra
Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
We show how to treat the constraints and reality conditions in the
-ADM (Ashtekar) formulation of general relativity, for the case of a
vacuum spacetime with a cosmological constant. We clarify the difference
between the reality conditions on the metric and on the triad. Assuming the
triad reality condition, we find a new variable, allowing us to solve the gauge
constraint equations and the reality conditions simultaneously.Comment: LaTeX file, 12 pages, no figures; to appear in Classical and Quantum
Gravit
Constraint propagation in the family of ADM systems
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 present constraint propagation equations and their eigenvalues
for the Arnowitt-Deser-Misner (ADM) evolution equations with additional
constraint terms (adjusted terms) on the right hand side. We conjecture that
the system is robust against violation of constraints if the amplification
factors (eigenvalues of Fourier-component of the constraint propagation
equations) are negative or pure-imaginary. We show such a system can be
obtained by choosing multipliers of adjusted terms. Our discussion covers
Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also
mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure