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Title: Gauge structure of the Einstein field equations in Bondi-like coordinates
Author: Giannakopoulos, Thanasis
Bishop, Nigel T.
Hilditch, David
Pollney, Denis
Zilhão, Miguel
Issue Date: 2022
Publisher: American Physical Society
Abstract: The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype formulations of this type are only weakly hyperbolic. Presently we examine the root cause of this result. In a linear analysis we identify the gauge, constraint and physical blocks in the principal part of the Einstein field equations in such a gauge, and show that the subsystem related to the gauge variables is only weakly hyperbolic. Weak hyperbolicity of the full system follows as a consequence in many cases. We demonstrate this explicitly in specific examples, and thus argue that Bondi-like gauges result in weakly hyperbolic free evolution systems under quite general conditions. Consequently the characteristic initial (boundary) value problem of GR in these gauges is rendered ill-posed in the simplest norms one would like to employ. The possibility of finding good alternative norms, in which well-posedness is achieved, is discussed. So motivated, we present numerical convergence tests with an implementation of full GR which demonstrate the effect of weak hyperbolicity in practice.
Peer review: yes
DOI: 10.1103/PhysRevD.105.084055
ISSN: 1550-7998
Appears in Collections:CIDMA - Artigos
GGDG - Artigos

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