Stability analysis of squashed Kaluza-Klein black holes with charge

作者：Nishikawa Ryusuke^*; Kimura Masashi

来源：Classical and Quantum Gravity, 2010, 27(21): 215020.

DOI：10.1088/0264-9381/27/21/215020

We study gravitational and electromagnetic perturbation around the squashed Kaluza-Klein black holes with charge. Since the black hole spacetime focused on in this paper has the SU(2) x U(1) similar or equal to U(2) symmetry, we can separate the variables of the equations for perturbations by using the Wigner function D-KM(J) which is the irreducible representation of the symmetry. In this paper, we mainly treat J = 0 modes which preserve the SU(2) symmetry. We derive the master equations for the J = 0 modes and discuss the stability of these modes. We show that the modes of J = 0 and K = 0, +/- 2 and the modes of K = +/-(J + 2) are stable against small perturbations from the positivity of the effective potential. As for J = 0, K = +/- 1 modes, since there are domains where the effective potential is negative except for the maximally charged case, it is difficult to show the stability of these modes in general. To show the stability for J = 0, K = +/- 1 modes in general is an open issue. However, we can show the stability for J = 0, K = +/- 1 modes in the maximally charged case where the effective potential is positive outside of the horizon.

• 出版日期2010-11-21