Highly accurate calculation of rotating neutron stars

Abstract

Abstract. We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate general-relativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, we show using representative examples, how the accuracy improves as the order of the approximation increases. As well as homogeneous fluid bodies, we also discuss models of polytropic and strange stars.

Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity

“…Because it resides on two critical curves we notice a loss in accuracy that was somewhat recovered by an extrapolation to an infinite approximation order m of the AKM method (cf. Ansorg et al 2003c). Observe also the unexpectedly high value for the red shift Z p of a photon emitted at one of the poles.…”

“…Taking into account asymptotic flatness, boundary and transition conditions at the surface and regularity along the rotational axis (ρ = 0), the interior and exterior field equations form a complete set of equations to be solved, which is done by applying the AKM method. For a comprehensive discussion of this multi domain spectral method see Ansorg et al (2003c).…”

“…-Mass shed parameter (as defined in Ansorg et al 2003c) where ζ s (ρ) is the function describing the surface shape. Maclaurin and Schwarzschild bodies are characterized by β = 1 and the mass shed limit is fixed by β = 0.…”

“…All five limiting curves were found to circumscribe entirely the general relativistic solution for homogeneous star models that are continuously joined to the static Schwarzschild solution -hereafter called the "generalized Schwarzschild solution" 2 . This was done using the recently developed AKM method (Ansorg et al 2002(Ansorg et al , 2003c, which allows one to solve the Einstein equations to high accuracy even for critical configurations. In particular we are able to determine to high precision the extreme configuration possessing both a mass shed and infinite central pressure.…”

Almost-Killing conserved currents: A general mass function

“…The essential tool for to identify jet formation in our numerical simulations was the energy flux density of the electromagnetic field. The spacetime geometry was given by a family of stationary and axisymmetric star models [2,3]. This allowed us to use the timelike Killing vector for constructing the energy-momentum conserved current of the electromagnetic field.…”