Viscosity driven instability in rotating relativistic stars

Abstract

We investigate the viscosity driven instability 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 those effects on the value of the threshold. For a uniformly rotating star, the criterion T /W , where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13 ∼ 0.16, which differ slightly 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. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

Gravitational wave content and stability of uniformly, rotating, triaxial neutron stars in general relativity

“…Here T is the kinetic energy and W the gravitational potential energy. In GR this critical value is higher [22][23][24][25][26][27][28]. The combination of the above characteristics imply that an evolutionary follow-up will also be nontrivial, since the first challenge described above will imply the presence of junk initial radiation, which must be controlled, while the second and third challenges require higher resolution than for slowly rotating stars.…”

Instabilities in rotating relativistic stars driven by viscosity

“…We then determine the stability of the star as follows. When the diagnostic q grows exponentially after we impose a bar mode perturbation in the logarithmic lapse, we conclude that the star is Table II of Saijo and Gourgoulhon 2006). Open circles, filled circles, open squares, and filled squares refer to the compactness M/R of 0.01, 0.05, 0.1, and 0.15, respectively.…”

“…5 we briefly summarize our findings. Throughout this paper, we use the geometrized units with G = c = 1 and adopt polar coordinates (r, θ, ϕ) with the coordinate time t. A more detailed discussion is presented in Saijo and Gourgoulhon (2006).…”

Dissipation-Induced Instability Phenomena in Infinite-Dimensional Systems

“…Indeed, infinite-dimensional dissipation-induced instabilities occur not only in fluid dynamics, but seem to be inherent in other field theories, for example general relativity [77] since the Einstein equations can be written in a form analogous to that of the NSEs, so that the dissipative effects become apparent [84].…”