Analysis of ``Gauge Modes'' in Linearized Relativity
Richard A. Matzner, Mijan Huq, Alonso Botero, Dae Il Choi, Ullar Kask,, Juan Lara, Steven Liebling, David Neilsen, Premana Premadi, Deirdre, Shoemaker
TL;DR
This paper analyzes gauge modes in linearized relativity by examining ADM equations, showing how gauge and constraint modes naturally arise and can be controlled in computational discretizations.
Contribution
It provides a detailed analysis of gauge and constraint modes in linearized ADM equations, clarifying their properties and how to manage them in numerical simulations.
Findings
Gauge and constraint modes are inherent in the ADM formulation of linearized relativity.
These modes can be controlled in well-designed computational discretizations.
The analysis aids in understanding initial data and evolution in linearized gravitational wave problems.
Abstract
By writing the complete set of (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations.
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