New Representation of some Static and Axisymmetric Vacuum Solutions

Details New Representation of some Static and Axisymmetric Vacuum Solutions New Representation of some Static and Axisymmetric Vacuum Solutions

2010-10-14

arxiv.org/abs/1010.2843v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to General Relativity and Gravitation

Scientific paper

We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical behaviour which can be written in a simple compact form, in terms of a function that must satisfies certain Cauchy-Newman problem. The relation between the choice of coordinates and the form of the metric functions that describe the solution is given by providing that analytic function which characterizes the metric as well as the gauge.

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