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http://hdl.handle.net/10773/35222
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 |
URI: | http://hdl.handle.net/10773/35222 |
DOI: | 10.1103/PhysRevD.105.084055 |
ISSN: | 1550-7998 |
Appears in Collections: | CIDMA - Artigos GGDG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2111.14794.pdf | 743.07 kB | Adobe PDF | View/Open |
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