The high-energy collision of black holes in higher dimensions

TL;DR

This paper calculates the gravitational wave energy emitted during head-on black hole collisions in higher dimensions up to 8D, revealing regimes of weak and exponential radiation growth with velocity, and estimating the maximum energy loss at relativistic speeds.

Contribution

It provides the first detailed computation of gravitational wave emission in higher-dimensional black hole collisions across a range of velocities and dimensions, extending previous 4D results.

Findings

Maximum radiation loss increases with dimension, reaching up to 12.9% in 8D.

Radiation is minimal for small but finite velocities, not at rest.

Exponential growth of radiated energy with velocity at high speeds.

Abstract

We compute the gravitational wave energy $E_{\rm rad}$ radiated in head-on collisions of equal-mass, nonspinning black holes in up to $D=8$ dimensional asymptotically flat spacetimes for boost velocities $v$ up to about $90\,\%$ of the speed of light. We identify two main regimes: Weak radiation at velocities up to about $40\,\%$ of the speed of light, and exponential growth of $E_{\rm rad}$ with $v$ at larger velocities. Extrapolation to the speed of light predicts a limit of $12.9\,\%$ $(10.1,~7.7,~5.5,~4.5)\,\%$. of the total mass that is lost in gravitational waves in $D=4$ $(5,\,6,\,7,\,8)$ spacetime dimensions. In agreement with perturbative calculations, we observe that the radiation is minimal for small but finite velocities, rather than for collisions starting from rest. Our computations support the identification of regimes with super Planckian curvature outside the black-hole horizons reported by Okawa, Nakao, and Shibata [Phys.~Rev.~D {\bf 83} 121501(R) (2011)].