The interior space-time metric for a rotating spherical star

[Gravitino]

I was looking for a space time metric that describes the INTERIOR of spherically symmetric rotating stars. However, wherever I look it is always the metric for an exterior of "slowly rotating star" (frame dragging effect) or something similar to it but always the metric AROUND the object (exterior). Is there any solution for interior of the star? I know already the interior Schwarzschild solution but is there the same for a rotating star? Thanks in advance.

 

[Max™]

Finding the interior solution for something approximating a Kerr Metric is an open problem, as I recall.

Good luck, and keep us informed?

 

[Mentz114]

These references have been passed on to me -

http://arxiv.org/abs/gr-qc/9910001
Michael Bradley, Gyula Fodor, Mattias Marklund, Zoltán Perjés
The Wahlquist metric cannot describe an isolated rotating body

http://arxiv.org/abs/gr-qc/0202065
R. J. Wiltshire
Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

http://arxiv.org/abs/gr-qc/0207099
Gyula Fodor, Zolt{á}n Perj{é}s, Michael Bradley
Slowly rotating charged fluid balls and their matching to an exterior domain

http://arxiv.org/abs/gr-qc/0304097
Ron Wiltshire
Slowly rotating, compact fluid sources embedded in Kerr empty space-time

http://arxiv.org/abs/gr-qc/0601024
Ron Wiltshire
Isotropy, shear, symmetry and exact solutions for relativistic fluid spheres

http://arxiv.org/abs/gr-qc/0612046
Michael Bradley, Daniel Eriksson, Gyula Fodor, Istvan Racz
Slowly rotating fluid balls of Petrov type D

 

[stevebd1]

It's fairly old but looks relevant-

'Simple Tests for Proposed Interior Metrics' by P. Collas
http://www.csun.edu/~vcphy00d/PDFPublications/1978 Collas tests.pdf

 

[stevebd1]

There's a typo in the above paper, qm/r₀ in equations (7) and (9) should read 9m/r₀ which is clarified on page 719 in the following extract from 'GR & Gravitation'-

'Trapped Null Geodesics in a Rotating Interior Metric' by P. Collas and J. K. Lawrence
http://www.csun.edu/~vcphy00d/PDFPublications/1976 Collas-Lawrence.pdf