Does a black hole rotate in Chern-Simons modified gravity?

TL;DR

This paper investigates rotating black hole solutions in Chern-Simons modified gravity, finding that rotation is generally suppressed for finite mass with a timelike embedding but possible in certain limits or with spacelike vectors.

Contribution

It provides a perturbative analysis of rotating black holes in Chern-Simons gravity, revealing conditions under which rotation can or cannot occur based on the embedding vector.

Findings

Rotation is suppressed for finite mass with a timelike embedding vector.

Rotation can occur in the limit of small mass or with a spacelike embedding vector.

The metric's zenith-angle dependence is derived independently of embedding coordinate choice.

Abstract

Rotating black hole solutions in the (3+1)-dimensional Chern-Simons modified gravity theory are discussed by taking account of perturbation around the Schwarzschild solution. The zenith-angle dependence of a metric function related to the frame-dragging effect is determined from a constraint equation independently of a choice of the embedding coordinate. We find that at least within the framework of the first-order perturbation method, the black hole cannot rotate for finite black hole mass if the embedding coordinate is taken to be a timelike vector. However, the rotation can be permitted in the limit of $M/r \to 0$ (where $M$ is the black hole mass and $r$ is the radius). For a spacelike vector, the rotation can also be permitted for any value of the black hole mass.