Abstract
We perform some numerical studies of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter We find that general relativity weakens the Jacobi-like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy for a compaction parameter as high as is only higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for is only larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.
- Received 23 May 2002
DOI:https://doi.org/10.1103/PhysRevD.66.044021
©2002 American Physical Society