New code for equilibriums and quasiequilibrium initial data of compact objects. III. Axisymmetric and triaxial rotating stars

We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.