456 research outputs found

### Stability of rigidly rotating relativistic stars with soft equations of state against gravitational collapse

We study secular stability against a quasi-radial oscillation for rigidly
rotating stars with soft equations of state in general relativity. The
polytropic equations of state with polytropic index $n$ between 3 and 3.05 are
adopted for modeling the rotating stars. The stability is determined in terms
of the turning-point method. It is found that (i) for n \agt 3.04, all the
rigidly rotating stars are unstable against the quasi-radial oscillation and
(ii) for n \agt 3.01, the nondimensional angular momentum parameter $q \equiv
cJ/GM^2$ (where $J$, $M$, $G$, and $c$ denote the angular momentum, the
gravitational mass, the gravitational constant, and the speed of light,
respectively) for all marginally stable rotating stars is larger than unity. A
semi-analytic calculation is also performed, and good agreement with the
numerical results is confirmed. The final outcome after axisymmetric
gravitational collapse of rigidly rotating and marginally stable massive stars
with $q > 1$ is predicted, assuming that the rest-mass distribution as a
function of the specific angular momentum is preserved and that the pressure
never halt the collapse. It is found that even for 1 < q \alt 2.5, a black
hole may be formed as a result of the collapse, but for q \agt 2.5, the
significant angular momentum will prevent the direct formation of a black hole.Comment: 23 pages, to be published in Ap

### Axisymmetric Simulations of Rotating Stellar Collapse in Full General Relativity --- Criteria for Prompt Collapse to Black Holes

Motivated by a recent paper by the Potsdam numerical relativity group, we
have constructed a new numerical code for hydrodynamic simulation of
axisymmetric systems in full general relativity. In this code, we solve the
Einstein field equation using Cartesian coordinates with appropriate boundary
conditions. On the other hand, the hydrodynamic equations are solved in
cylindrical coordinates. Using this code, we perform simulations to study
axisymmetric collapse of rotating stars, which thereby become black holes or
new compact stars, in full general relativity. To investigate the effects of
rotation on the criterion for prompt collapse to black holes, we first adopt a
polytropic equation of state, $P=K\rho^{\Gamma}$, where $P$, $\rho$, and $K$
are the pressure, rest mass density, and polytropic constant, with $\Gamma=2$.
In this case, the collapse is adiabatic (i.e., no change in entropy), and we
can focus on the bare effect of rotation. As the initial conditions, we prepare
rigidly and differentially rotating stars in equilibrium and then decrease the
pressure to induce collapse. In this paper, we consider cases in which $q
\equiv J/M_g^2 < 1$, where $J$ and $M_g$ are the angular momentum and the
gravitational mass. It is found that the criterion of black hole formation is
strongly dependent on the angular momentum parameter $q$. For $q < 0.5$, the
criterion is not strongly sensitive to $q$; more precisely, if the rest mass is
slightly larger than the maximum allowed value of spherical stars, a black hole
is formed. However, for q \alt 1, it changes significantly: For $q \simeq
0.9$, the maximum allowed rest mass becomes $\sim 70$ - 80% larger than that
for spherical stars.Comment: 41 pages, to appear in Prog. Theor. Phys. 104, Augus

### Close-slow analysis for head-on collision of two black holes in higher dimensions: Bowen-York initial data

Scenarios of large extra dimensions have enhanced the importance for the
study of black holes in higher dimensions. In this paper, we analyze an
axisymmetric system of two black holes. Specifically, the Bowen-York method is
generalized for higher dimensions in order to calculate the initial data for
head-on collision of two equal-mass black holes. Then, the initial data are
evolved adopting the close-slow approximation to study gravitational waves
emitted during the collision. We derive an empirical formula for radiation
efficiency, which depends weakly on the dimensionality. Possible implications
of our results for the black hole formation in particle colliders are
discussed.Comment: 28 pages, 7 figures, published versio

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