On the uniqueness of harmonic coordinates

Details On the uniqueness of harmonic coordinates On the uniqueness of harmonic coordinates

2005-03-04

arxiv.org/abs/gr-qc/0503018v1

Czech.J.Phys. 55 (2005) 105-118

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, no figures

Scientific paper

10.1007/s10582-005-0024-z

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.

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