Boosting Taub-NUT to a BPS NUT-wave

TL;DR

This paper explores the properties of boosted Taub-NUT metrics, revealing a dual momentum and deriving a shock pp-wave with NUT charge as a gravitational dual to the boosted Schwarzschild solution, also showing its BPS nature.

Contribution

It introduces a dual momentum vector in linearized gravity for NUT charge and derives a new shock pp-wave as its infinite boost limit, establishing its BPS status.

Findings

The boosted Taub-NUT metric exhibits a dual momentum in the boost direction.

The infinite boost limit yields a shock pp-wave with NUT charge.

The shock pp-wave is a half-BPS solution in N=1 supergravity.

Abstract

The boosted Taub-NUT metric with zero ADM mass is shown to possess a dual momentum in the direction of the boost giving credit to the existence of another 4-vector K_\mu in linearized gravity associated to the NUT charge and dual to the usual P_\mu. Taking the infinite boost limit we obtain a shock pp-wave with NUT charge. We show that the latter is the gravitational dual of the infinitely boosted Schwarzschild metric, also known as the Aichelburg-Sexl pp-wave. We review the fact that this new shock pp-wave is also an half-BPS solution of N=1 supergravity. It has a BPS bound equal to K_t=|K_z|.