An analytical scheme and a numerical method in order to study the effects of general relativity on the viscosity driven secular bar mode instability of rapidly rotating stars are presented .
The approach consists in perturbing an axisymmetric and stationary configuration and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations .
These are obtained by solution of an approximate set of field equations where only the dominant non-axisymmetric terms are taken into account .
The progress with respect to our former investigation consists in a higher relativistic order of the non-axisymmetric terms included into the computation , namely the fully three-dimensional treatment of the vector part of the space-time metric tensor as opposed to the scalar part , solely , in the former case .
The scheme is applied to rotating stars built on a polytropic equation of state and compared to our previous results .
The 3D-vector part turns out to inhibit the symmetry breaking efficiently .
Nevertheless , the bar mode instability is still possible for an astrophysically relevant mass of M _ { ns } = 1.4 M _ { \sun } when a stiff polytropic equation of state with an adiabatic index of \gamma = 2.5 is employed .
Triaxial neutron stars may be efficient emitters of gravitational waves and are thus potentially interesting sources for the forthcoming laser interferometric gravitational wave detectors such as LIGO , VIRGO and GEO600 .
From a numerical point of view , the solution of the three-dimensional minimal-distortion shift vector equation in spherical coordinates is an important achievement of our code .