Understand
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).
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