Positive energy theorem implies constraints on static steller models

Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain conditions on the equation of state. As the contraposition, we obtain some constraints on the pressure and adiabatic index.Comment: 7 pages, final version accepted for publication in Prog. Theore. Phy

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

Distorted static photon surfaces in perturbed Reissner-Nordstr\"om spacetimes

The photon surface is defined as a timelike surface $S$ such that any photon emitted in arbitrary tangential direction to $S$ from an arbitrary point on $S$ continues to propagate on $S$. In this paper, we examine whether a static photon surface can be present in distorted electrovacuum spacetimes with perturbative approach, by constructing analytic solutions to the equations for static perturbations of a Reissner-Nordstr\"om spacetime that are regular outside the background photon surface. For each of the $\ell\ge 2$ modes, there are two physical solutions to the perturbative equations that correspond to adding the multipole moments of mass and electric charge, respectively. By adjusting the ratio of the amplitudes of the two solutions appropriately, it is possible to realize a distorted photon surface. In the case of $\ell=1$, although there is only one physical solution to the perturbative equations, there is also a degree of freedom to shift the coordinate position of the photon surface, and this enables the formation of a photon surface. Such a photon surface has a spherically symmetric spatial section, but it is also distorted in the three-dimensional sense. Our results show that distorted static photon surfaces can be formed at least at the level of the first-order perturbations, and imply that the uniqueness of the photon surface may not hold in electrovacuum spacetimes.Comment: 40 pages , 5 figure

On existence of matter outside a static black hole

It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of matter composed of a perfect fluid in static black hole spacetimes under certain conditions, which can be interpreted as a relation between the stellar mass and the black hole mass.Comment: 4pages, final version accepted for publication in Journal of Mathematical Physic