Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity , assuming a conformally flat spatial geometry ( Isenberg-Wilson-Mathews formulation ) and a polytropic equation of state .
Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids , centered at the source , in all angular directions up to a large truncation radius .
Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations .
Selected parameters are to model ( proto- ) neutron stars ; the compactness is M / R = 0.001 , 0.1 , 0.14 , 0.2 for polytropic index n = 0.3 and M / R = 0.001 , 0.1 , 0.12 , 0.14 for n = 0.5 .
We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes .
However , it is also found that the triaxial sequences become shorter for higher compactness , and those may disappear at a certain large compactness for the n = 0.5 case .
In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling , it is plausible that , once the viscosity driven secular instability sets in during the contraction , the proto-neutron stars are always maximally deformed triaxial configurations , as long as the compactness and the equation of state parameters allow such triaxial sequences .
Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state .