Higher dimensional Numerical Relativity: code comparison

TL;DR

This paper compares two numerical relativity codes for simulating higher-dimensional black hole collisions, demonstrating their agreement and providing precise measurements of gravitational radiation in five and six dimensions.

Contribution

It presents a direct comparison of two successful codes for higher-dimensional Einstein equations, confirming their consistency and accuracy in black hole collision simulations.

Findings

Codes agree to numerical precision in collision simulations

Total radiated energy in five dimensions: 9x10^{-4} M

Total radiated energy in six dimensions: 8.1x10^{-4} M

Abstract

The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in six dimensions.