Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-03-05
Class.Quant.Grav.25:228002,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, 2 figures
Scientific paper
10.1088/0264-9381/25/22/228002
We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star that has been constructed numerically in the former coordinates with an axially symmetric stationary metric that is given through an analytical form in the latter coordinates. Since a stationary metric associated with an isolated object that is built numerically partly refers to a non-vacuum solution (interior of the star) the transformation of its coordinates to Weyl-Papapetrou coordinates, which are usually used to describe vacuum axisymmetric and stationary solutions of Einstein equations, is not straightforward in the non-vacuum region. If this point is \textit{not} taken into consideration, one may end up to erroneous conclusions about how well a specific analytical metric matches the metric around the star, due to fallacious coordinate transformations.
Apostolatos Theocharis A.
Pappas George
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