Stability analysis of Squashed Kaluza-Klein Black Holes with Charge

Understand

We study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge.

• Since the black hole spacetime focused on this paper have $SU(2) \times U(1) \simeq U(2)$ symmetry, we can separate the variables of the equations for perturbations by using Wigner function $D^{J}_{KM}$ which is the irreducible representation of the symmetry.
• In this paper, we mainly treat $J=0$ modes which preserve $SU(2)$ symmetry.
• We derive the master equations for the $J=0$ modes and discuss the stability of these modes.