I am confused as to what the Chandrasekhar-Friedman-Schutz (CFS) instability is, exactly.
It seems to partially refer to this paper (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.24.611) by Chandrasekhar, but I do not think this paper covers the full instability. In the first part of the paper, Chandrasekhar shows that a Jacobi ellipsoid radiates off angular momentum in gravitational waves to become a Maclauren ellipsoid. I do not yet understand the second part of the paper.
This webpage (http://www.personal.soton.ac.uk/dij/cfs.html) says that in a rotating star, a non axially symmetric perturbation rotating slower than a star will radiate off angular momentum, thus increasing the size of the perturbation. Apparently, any rotating star is unstable in general relativity. Obviously, rotating stars do exist. Somehow, I think damping effects in an actual star work against the instability for slowly rotating stars, but can't fight the instability for fast rotating stars. (?)
As is clear, I am very confused as to what the exact nature of the instability is. Do quickly rotating stars collapse into black holes, or do they just radiate off angular momentum and settle down into slowly rotating stars? Have we detected this instability experimentally in the real world?
Also, is there a good source that gives an introduction to the instability? Papers by Friedman and Shutz (like this http://adsbit.harvard.edu//full/1978ApJ...222..281F/0000291.000.html) seem to focus heavily on obtuse mathematics (i.e. "trivial" Lagrangian perturbations) and don't present a clear physical picture of what the instability actually is.