Rotating Carroll Black Holes: A No Go Theorem

TL;DR

This paper proves that in higher-dimensional Carrollian gravity, stationary axisymmetric solutions are necessarily static, with special cases allowing for rotation in three dimensions, and extends the no-go theorem to include various matter fields.

Contribution

It establishes a no-go theorem for rotating Carroll black holes in higher dimensions and explores exceptions in three dimensions and with additional matter fields.

Findings

Higher-dimensional Carroll black holes are necessarily static if stationary and axisymmetric.

In 3D, rotating Carroll black holes can exist via Carroll boosts and re-identification.

A Carrollian analogue of an accelerating black hole is also constructed.

Abstract

Recently, there has been a lot of interest in Carroll black holes and in particular whether or not one could find a Carrollian analogue of a rotating black hole spacetime. Here we show that every stationary and axisymmetric solution (and thence also a black hole) of Carrollian general relativity in any number of $d>3$ dimensions is necessarily also static (up to a "topological rotation"). The case of $d=3$ dimensions is special. There, the topological rotation is important and one can have a rotating Carroll BTZ black hole, obtained from a static one by the Carroll boost accompanied by the re-identification of the angular coordinate, similar to what happens in the Lorentzian case. We also find a Carrollian analogue of an accelerating black hole, showing that Schwarzschild is not the only possible stationary and axisymmetric Carroll black hole in four dimensions. A generalization of the no go theorem to include Maxwell, dilatonic, and axionic matter fields is also discussed.