### Abstract

We investigate the instability driven by viscosity in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study these factors on the critical value T/W for the instability. For a rigidly rotating star, the criterion T/W, where T is the rotational kinetic energy and W the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13-0.16, which slightly differ from that of Newtonian incompressible stars (∼0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17-0.25. The value is significantly larger than in the rigidly rotating case with the same compactness of the star. Finally we discuss the possibility of detecting gravitational waves from viscosity-driven instabilities using ground-based interferometers.

Original language | English |
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Title of host publication | Isolated Neutron Stars: From The Surface To The Interior |

Publisher | Springer Netherlands |

Pages | 481-485 |

Number of pages | 5 |

ISBN (Print) | 9781402059971 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

### Keywords

- Gravitational waves
- Instabilities
- Relativity
- Stars: rotation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Isolated Neutron Stars: From The Surface To The Interior*(pp. 481-485). Springer Netherlands. https://doi.org/10.1007/978-1-4020-5998-8-62