  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.
