Can rigidly rotating polytropes be sources of the Kerr metric?

Abstract

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.

arXiv commentLaTeX, 17 pages, submitted to CQG

References in corpus (5)

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Cited by in corpus (5)

• The quadrupole moment of slowly rotating fluid balls
• On the asymptotic behavior of static perfect fluids
• An approximate global solution of Einstein's equation for a rotating compact source with linear equation of state
• Wahlquist's metric versus an approximate solution with the same equation of state
• An approximate global solution of Einstein's equations for differentially rotating compact body