Improved analysis of black hole formation in high-energy particle collisions

We investigate formation of an apparent horizon (AH) in high-energy particle collisions in four- and higher-dimensional general relativity, motivated by TeV-scale gravity scenarios. The goal is to estimate the prefactor in the geometric cross section formula for the black hole production. We numerically construct AHs on the future light cone of the collision plane. Since this slice lies to the future of the slice used previously by Eardley and Giddings [Phys. Rev. D 66, 044011 (2002)] and by one of us and Nambu [Phys. Rev. D 67, 024009 (2003)], we are able to improve the prefactor estimates. The black hole production cross section increases by 40%\char21{}70% in the higher-dimensional cases, indicating larger black hole production rates in future-planned accelerators than previously estimated. We also determine the mass and the angular momentum of the final black hole state, as allowed by the area theorem.