Black ring formation in particle systems

It is known that the formation of apparent horizons with nonspherical topology is possible in higher-dimensional spacetimes. One of these is the black ring horizon with [Formula Presented] topology where [Formula Presented] is the spacetime dimension number. In this paper, we investigate the black ring horizon formation in systems with [Formula Presented]-particles. We analyze two kinds of system: the high-energy [Formula Presented]-particle system and the momentarily-static [Formula Presented]-black hole initial data. In the high-energy particle system, we prove that the black ring horizon does not exist at the instant of collision for any [Formula Presented]. But there remains a possibility that the black ring forms after the collision and this result is not sufficient. Because calculating the metric of this system after the collision is difficult, we consider the momentarily-static [Formula Presented]-black hole initial data that can be regarded as a simplified [Formula Presented]-particle model and numerically solve the black ring horizon that surrounds all the particles. Our results show that there is the minimum particle number that is necessary for the black ring formation and this number depends on [Formula Presented]. Although many particle number is required in five-dimensions, [Formula Presented] is sufficient for the black ring formation in the [Formula Presented] cases. The black ring formation becomes easier for larger [Formula Presented]. We provide a plausible physical interpretation of our results and discuss the validity of Ida and Nakao’s conjecture for the horizon formation in higher-dimensions. Finally we briefly discuss the probable methods of producing the black rings in accelerators.