Numerical relativity for D dimensional space-times: Head-on collisions of black holes and gravitational wave extraction

Abstract

Higher dimensional black holes play an exciting role in fundamental physics, such as high energy physics. In this paper, we use the formalism and numerical code reported in [1] to study the head-on collision of two black holes. For this purpose we provide a detailed treatment of gravitational wave extraction in generic D dimensional space-times, which uses the Kodama-Ishibashi formalism. For the first time, we present the results of numerical simulations of the head-on collision in five space-time dimensions, together with the relevant physical quantities. We show that the total radiated energy, when two black holes collide from rest at infinity, is approximately (0.089 ± 0.006)% of the center of mass energy, slightly larger than the 0.055% obtained in the four-dimensional case, and that the ringdown signal at late time is in very good agreement with perturbative calculations.