59 research outputs found

### The Parametric Transition of Strange Matter Rings to a Black Hole

It is shown numerically that strange matter rings permit a continuous
transition to the extreme Kerr black hole. The multipoles as defined by Geroch
and Hansen are studied and suggest a universal behaviour for bodies approaching
the extreme Kerr solution parametrically. The appearance of a `throat region',
a distinctive feature of the extreme Kerr spacetime, is observed. With regard
to stability, we verify for a large class of rings, that a particle sitting on
the surface of the ring never has enough energy to escape to infinity along a
geodesic.Comment: 16 pages, 11 figures, v3: minor changes so as to coincide with
published versio

### Thermodynamic Description of Inelastic Collisions in General Relativity

We discuss head-on collisions of neutron stars and disks of dust ("galaxies")
following the ideas of equilibrium thermodynamics, which compares equilibrium
states and avoids the description of the dynamical transition processes between
them. As an always present damping mechanism, gravitational emission results in
final equilibrium states after the collision. In this paper we calculate
selected final configurations from initial data of colliding stars and disks by
making use of conservation laws and solving the Einstein equations. Comparing
initial and final states, we can decide for which initial parameters two
colliding neutron stars (non-rotating Fermi gas models) merge into a single
neutron star and two rigidly rotating disks form again a final (differentially
rotating) disk of dust. For the neutron star collision we find a maximal energy
loss due to outgoing gravitational radiation of 2.3% of the initial mass while
the corresponding efficiency for colliding disks has the much larger limit of
23.8%.Comment: 25 pages, 9 figure

### Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids

We give a thorough investigation of sequences of uniformly rotating,
homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate
from highly flattened Maclaurin spheroids. Each one of these sequences
possesses a mass-shedding limit. Starting at this point, the sequences proceed
towards the Maclaurin sequence and beyond. The first sequence leads to the well
known Dyson rings, whereas the end points of the higher sequences are
characterized by the formation of a two-body system, either a core-ring system
(for the second, the fourth etc. sequence) or a two-ring system (for the third,
the fifth etc. sequence). Although the general qualitative picture drawn by
Eriguchi and Hachisu in the eighties has been confirmed, slight differences
turned out in the interpretation of the origin of the first two-ring sequence
and in the general appearance of fluid bodies belonging to higher sequences.Comment: 10 pages, 11 figures, 5 tables, submitted to MNRA

### Uniformly Rotating Rings in General Relativity

In this paper, we discuss general relativistic, self-gravitating and
uniformly rotating perfect fluid bodies with a toroidal topology (without
central object). For the equations of state describing the fluid matter we
consider polytropic as well as completely degenerate, perfect Fermi gas models.
We find that the corresponding configurations possess similar properties to the
homogeneous relativistic Dyson rings. On the one hand, there exists no limit to
the mass for a given maximal mass-density inside the body. On the other hand,
each model permits a quasistationary transition to the extreme Kerr black hole.Comment: 6 pages, 4 figures, added material and one new referenc

### A universal inequality between angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

We prove that for sub-extremal axisymmetric and stationary black holes with
arbitrary surrounding matter the inequality $8\pi|J|<A$ holds, where $J$ is the
angular momentum and $A$ the horizon area of the black hole.Comment: 8 page

### On the Solution Space of Differentially Rotating Neutron Stars in General Relativity

A highly accurate, multi-domain spectral code is used in order to construct
sequences of general relativistic, differentially rotating neutron stars in
axisymmetry and stationarity. For bodies with a spheroidal topology and a
homogeneous or an N=1 polytropic equation of state, we investigate the solution
space corresponding to broad ranges of degree of differential rotation and
stellar densities. In particular, starting from static and spherical
configurations, we analyse the changes of the corresponding surface shapes as
the rate of rotation is increased. For a sufficiently weak degree of
differential rotation, the sequences terminate at a mass-shedding limit, while
for moderate and strong rates of differential rotation, they exhibit a
continuous parametric transition to a regime of toroidal fluid bodies. In this
article, we concentrate on the appearance of this transition, analyse in detail
its occurrence and show its relevance for the calculation of astrophysical
sequences. Moreover, we find that the solution space contains various types of
spheroidal configurations, which were not considered in previous work, mainly
due to numerical limitations.Comment: 9 pages, 10 figures, version to be published in MNRAS ; no major
changes with respect to v1: title, abstract and other things were modified to
put more emphasis on general aspects of the wor

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