Action Principle for the Generalized Harmonic Formulation of General Relativity
J. David Brown
TL;DR
This paper introduces an action principle for the generalized harmonic formulation of general relativity, linking it to the Z4 formulation and providing a foundational theoretical framework.
Contribution
It presents a new action principle for the generalized harmonic formulation, expanding the theoretical tools available for analyzing general relativity.
Findings
Derived the action functional for the generalized harmonic formulation.
Analyzed the relationship between the generalized harmonic and Z4 formulations.
Discussed implications for theoretical and numerical relativity.
Abstract
An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.
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