Ultrarelativistic boost of the black ring

TL;DR

This paper studies the ultrarelativistic limit of a five-dimensional black ring, revealing how its gravitational field transforms into impulsive waves with ring or rod-shaped singularities depending on the boost direction.

Contribution

It extends the classical Aichelburg-Sexl method to five-dimensional black rings, analyzing the resulting impulsive pp-waves and their singularity structures for different boost directions.

Findings

Black ring boosts produce impulsive pp-waves in five dimensions.

Singularities become ring or rod-shaped sources in the wave front.

Orthogonal boost retains a disk-shaped membrane component.

Abstract

We investigate the ultrarelativistic boost of the five-dimensional Emparan-Reall non-rotating black ring. Following the classical method of Aichelburg and Sexl, we determine the gravitational field generated by a black ring moving ``with the speed of light'' in an arbitrary direction. In particular, we study in detail two different boosts along axes orthogonal and parallel to the plane of the ring circle, respectively. In both cases, after the limit one obtains a five-dimensional impulsive pp-wave propagating in Minkowski spacetime. The curvature singularity of the original static spacetime becomes a singular source within the wave front, in the shape of a ring or a rod according to the direction of the boost. In the case of an orthogonal boost, the wave front contains also a remnant of the original disk-shaped membrane as a component of the Ricci tensor (which is everywhere else vanishing). We also analyze the asymptotic properties of the boosted black ring at large spatial distances from the singularity, and its behaviour near the sources. In the limit when the singularity shrinks to a point, one recovers the well known five-dimensional analogue of the Aichelburg-Sexl ``monopole'' solution.