Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity

Abstract

Abstract. Using a multi domain spectral method, we investigate systematically the general-relativistic model for axisymmetric uniformly rotating, homogeneous fluid bodies generalizing the analytically known Maclaurin and Schwarzschild solutions. Apart from the curves associated with these solutions and a further curve of configurations that rotate at the mass shedding limit, two more curves are found to border the corresponding two parameter set of solutions. One of them is a Newtonian lens shaped sequence bifurcating from the Maclaurin spheroid sequence, while the other one corresponds to highly relativistic bodies with an infinite central pressure. The properties of the configuration for which both the gravitational and the baryonic masses, moreover angular velocity, angular momentum as well as polar red shift obtain their maximal values are discussed in detail. In particular, by comparison with the static Schwarzschild solution, we obtain an increase of 34.25% in the gravitational mass. Moreover, we provide exemplarily a discussion of angular velocity and gravitational mass on the entire solution class.

Uniformly rotating rings in general relativity

“…In particular, for spherically symmetric static bodies Z 0 < 2 always holds, which is a consequence of the well‐known Buchdahl limit. Numerical investigations have shown that Z 0 < 7.378 for the class of uniformly rotating homogeneous spheroidal bodies (Schöbel & Ansorg 2003). The corresponding critical configuration with this maximal redshift rotates at the mass‐shedding limit and possesses infinite central pressure.…”

Rotating Stars in Relativity

“…Applying this new method to the computation of rapidly rotating homogeneous relativistic stars, Ansorg et al achieve near machine accuracy, except for configurations at the mass-shedding limit (see Section 2.7.8)! The code has been used in a systematic study of uniformly rotating homogeneous stars in general relativity [265]. …”

Slowly rotating homogeneous stars and the Heun equation

“…Such solutions were studied in [22] and termed the 'generalized Schwarzschild' class of solutions. A sequence of stars from this class with constant massM < 4/9R S ≈ 0.145 can be followed from the non-rotating limit to the mass-shedding limit, at which a cusp forms along the equatorial rim.…”