Generating Rotation in a Snap

TL;DR

The paper introduces a purely algebraic method to generate rotating solutions from static ones in higher-dimensional spacetimes, avoiding Einstein equation solutions.

Contribution

It presents a novel algebraic technique for constructing rotating geometries from static solutions in higher dimensions, applicable to various supergravity frameworks.

Findings

Recovered Kerr and Myers-Perry black holes from Schwarzschild solutions.

Derived a linear ansatz for multiple non-extremal rotating and charged sources.

Provided a systematic approach to generate non-extremal rotating geometries.

Abstract

We build a new technique to generate rotation from arbitrary static solutions that asymptote to four- or five-dimensional Minkowski spacetime. The method is purely algebraic and does not require solving Einstein equations. It proceeds by transforming the static solution to AdS$\times$S asymptotics, performing a coordinate shift to a uniformly rotating frame, and then transforming the solution back to asymptotically flat spacetime. We implement this construction in five-dimensional minimal supergravity, although it applies more broadly to any framework admitting AdS$\times$S geometries and relevant sigma-model transformations. As a first application, we recover simply the Kerr and Myers-Perry black holes directly from Schwarzschild black holes. We then apply the method to the linear class of static Weyl solutions and obtain the first linear ansatz describing an arbitrary number of non-extremal rotating and charged sources. This approach provides a systematic and simple route to constructing non-extremal rotating geometries in four and five dimensions.