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Czechoslovak Journal of Physics

, Volume 55, Issue 2, pp 105–118 | Cite as

On the uniqueness of harmonic coordinates

  • Jiří Bičák
  • Joseph Katz
Article

Abstract

Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose across the material boundary, and on the conditions at infinity and at a suitable point inside the matter. This is illustrated in detail by simple fully solvable examples of static spherically symmetric spacetimes in global harmonic coordinates. Examples of stationary electrovacuum spacetimes described simply in harmonic coordinates are also given. They can represent the exterior fields of material discs.

The use of an appropriate background metric considerably simplifies the calculations.

Key words

harmonic coordinates stationary metrics and their sources 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Jiří Bičák
    • 1
    • 2
  • Joseph Katz
    • 1
    • 3
  1. 1.Institute of AstronomyThe ObservatoriesCambridgeUK
  2. 2.Institute of Theoretical Physics, Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  3. 3.Racah Institute of PhysicsThe Hebrew UniversityJerusalemIsrael

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