Can rigidly rotating polytropes be sources of the Kerr metric?

Details Can rigidly rotating polytropes be sources of the Kerr metric? Can rigidly rotating polytropes be sources of the Kerr metric?

2007-09-07

arxiv.org/abs/0709.1119v1

Class.Quant.Grav.25:105019,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 17 pages, submitted to CQG

Scientific paper

10.1088/0264-9381/25/10/105019

We use a recent result by Cabezas et al. to build up an approximate solution to the gravitational field created by a rigidly rotating polytrope. We solve the linearized Einstein equations inside and outside the surface of zero pressure including second-order corrections due to rotational motion to get an asymptotically flat metric in a global harmonic coordinate system. We prove that if the metric and their first derivatives are continuous on the matching surface up to this order of approximation, the multipole moments of this metric cannot be fitted to those of the Kerr metric.

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