Ultrarelativistic limits of boosted dilaton black holes

TL;DR

This paper studies the ultrarelativistic limits of various dilaton black hole and black p-brane solutions, revealing shock wave and plane-fronted wave geometries as the boost velocity approaches the speed of light.

Contribution

It provides a comprehensive analysis of the ultrarelativistic limits of dilaton black objects, including multi-centered solutions and the influence of the dilaton field on these limits.

Findings

Black holes and p-branes become shock wave geometries at ultrarelativistic speeds.

Multi-centered solutions lead to multiple shock wave geometries.

Dilaton field affects the structure of the resulting wave solutions.

Abstract

We investigate the ultrarelativistic limits of dilaton black holes, black $p$-branes (strings), multi-centered dilaton black hole solutions and black $p$-brane (string) solutions when the boost velocity approaches the speed of light. For dilaton black holes and black $p$-branes (boost is along the transverse directions), the resulting geometries are gravitational shock wave solutions generated by a single particle and membrane. For the multi-centered dilaton black hole solutions and black $p$-brane solutions (boost is along the transverse directions), the limiting geometries are shock wave solutions generated by multiple particles and membranes. When the boost is along the membrane directions, for the black $p$-brane and multi-centered black $p$-brane solution, the resulting geometries describe general plane-fronted waves propagating along the membranes. The effect of the dilaton on the limit is considered.