Equilibrium configurations of homogeneous fluids in general relativity

Abstract

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core–ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust

On the solution space of differentially rotating neutron stars in general relativity

“…Other branches of this particular separatrix are formed by the Maclaurin spheroids with r p / r e ∈[0.111 60, 0.171 26] and the (non‐relativistic) Dyson ring sequence (marked by A ± 1 in fig. 4 of Ansorg et al 2004).…”

“…For homogeneous and rigidly rotating fluid bodies in general relativity, the Newtonian limiting sequences have been found to be the separatrix sequences that separate the general‐relativistic solution classes from one another (see Ansorg et al 2004, figs 4 and 5 therein). Specifically, the Maclaurin spheroids with r p / r e ∈[0.171 26, 1] form one branch of the separatrix dividing the spheroidal from the toroidal class.…”

“…However, the full solution space is much richer as it contains infinitely many Newtonian sequences that branch off from the Maclaurin sequence (see Ansorg, Kleinwächter & Meinel 2003b). Taking these configurations into the realm of general relativity, one recognizes the entire complexity of the solution space which turns out to consist of infinitely many disjoint solution classes (see Ansorg et al 2004). Within these classes (which are two‐dimensional subsets of the solution space), specific sections of the above Newtonian sequences form particular limiting curves.…”

Reference Ellipsoid and Geoid in Chronometric Geodesy

“…Post-Newtonian equilibrium configurations of uniformly rotating fluids have been discussed in literature by researchers from USA (Chandrasekhar, 1965(Chandrasekhar, , 1967a(Chandrasekhar, ,b,c, 1971aBardeen, 1971;Elbert, 1974, 1978;Chandrasekhar and Miller, 1974), Lithuania Pyragas et al, 1974Pyragas et al, , 1975, USSR (Tsirulev and Tsvetkov, 1982a,b;Tsvetkov and Tsirulev, 1983;Galtsov et al, 1984) and, the most recently, scientists from the Fridrich Schiller University of Jena in Germany (Petroff, 2003;Ansorg et al, 2004;Meinel et al, 2008;Petroff, 2010, 2013). These papers focused primarily on studying the astrophysical aspects of the problem like stability of the rotating stars, the points of bifurcations, exact axially-symmetric spacetimes, emission of gravitational waves, etc.…”

The parametric transition of strange matter rings to a black hole

“…To study quasi-stationary transitions that lead to black holes, we use bodies with a ring topology, since spheroidal bodies do not seem to have stationary sequences that lead to black holes [8]. For spheroidal bodies, a finite upper bound is observed for Z 0 , which is the relative redshift of zero angular momentum photons emitted from the surface of the body and observed at infinity.…”