Perturbative stability analysis of higher dimensional rotating black holes

We review the stability analysis of Myers-Perry black holes. The D-dimensional Myers- Perry spacetime has spherical horizon and is parametrized by its mass and n = [(D - 1)/2] angular momenta. In general, the spacetime has Rt × U(1)n isometry group, which corresponds to time translation and rotational symmetries. This symmetry is not enough to separate the gravitational perturbation equations and the perturbation equations are given by partial differential equations of (D - n - 1) coordinates. However, for special values of the angular momentum, the symmetry of the spacetime can be enhanced and it makes the stability analysis easy. In this paper, we focus on two kinds of Myers-Perry black holes. The first one is odd dimensional Myers-Perry black holes with equal angular momenta. This spacetime is cohomogeneity-1, namely, it depends on a single radial coordinate. In this spacetime, gravitational perturbation equations reduce to system of ordinary differential equations. In five dimensions, we find that there is no evidence of instability. On the other hand, for D = 7, 9, 11, 13, we see that the spacetime becomes unstable for large angular momenta. The second spacetime is singly rotating Myers-Perry black holes. This spacetime is cohomogeneity-2, namely, it depends on two coordinates. In this spacetime, the gravitational perturbation equation is given by 2-dimensional partial differential equations. We see the numerical evidence of the instability of this spacetime. At the onset of the instability of these spacetimes, there are statinary perturbations. Thus, these results indicate existence of new phases of rotating black holes in higher dimensions.