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