Instabilities in rotating relativistic stars driven by viscosity

Motoyuki Saijo*, Eric Gourgoulhon

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


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 languageEnglish
Title of host publicationIsolated Neutron Stars: From The Surface To The Interior
PublisherSpringer Netherlands
Number of pages5
ISBN (Print)9781402059971
Publication statusPublished - 2007
Externally publishedYes


  • Gravitational waves
  • Instabilities
  • Relativity
  • Stars: rotation

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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