Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics

Abstract

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.

arXiv comment18 pages, 2 figures

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• An accurate metric for the spacetime around neutron stars
• The exterior field of slowly and rapidly rotating neutron stars: Rehabilitating spacetime metrics involving hyperextreme objects
• Matching of analytical and numerical solutions for neutron stars of arbitrary rotation