Stability analysis of squashed Kaluza–Klein black holes with charge

Abstract

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) × U (1) ≃ 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. 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 maximally charged case, it is hard to show the stability of these modes in general. To show stability for J = 0, K = ±1 modes in general is open issue. However, we can show the stability for J = 0, K = ±1 modes in maximally charged case where the effective potential are positive out side of the horizon.call the higher-dimensional black holes on the spacetime with compact extra dimensions Kaluza-Klein black holes. In general, it is difficult to construct exact solutions describing Kaluza-Klein black holes because of the less symmetry than the asymptotically flat case.However, if we consider the spacetime with twisted extra-dimensions, we can construct such exact solutions, i.e. squashed Kaluza-Klein (SqKK) black holes [27,28] in the class of cohomogeneity-one symmetry. The topology of the horizon of this SqKK black holes is S 3 , while it looks like four-dimensional black holes with a circle as an internal space in the asymptotic region.Recently, much effort has been devoted to reveal the properties of squashed Kaluza-Klein black holes. In [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] generalizations of SqKK black holes are studied. Several aspects of SqKK black holes are also discussed, e.g. thermodynamics [48-50], Hawking radiation [51-53], gravitational collapse [54], behavior of Klein-Gordon equation [55], stabil-

Tunnelling of scalar and Dirac particles from squashed charged rotating Kaluza–Klein black holes

“…Different aspects of Kaluza-Klein black holes were also considered, namely thermodynamics [39][40][41], Hawking radiation and the tunnelling method [42][43][44][45][46][47][48], quasinormal modes and stabilities [49][50][51][52][53], geodetic precession [54] and gravitational lensing [55].…”

Stability analysis of black holes by the S -deformation method for coupled systems

“…The gravitational and electro-magnetic perturbation around the charged squashed Kaluza-Klein black hole was discussed in [22], and the master equations for K = ±1 mode perturbations take the same form as Eqs. (11) and (12), with d/dx = (F/K 2 )d/dρ.…”

“…(11) and (12), with d/dx = (F/K 2 )d/dρ. The explicit form of the effective potential is given in [22]. corresponding charge is Q/Q extremal = 0, 0.01, 0.5, 0.99, 1 from left to right, respectively.…”

“…corresponding charge is Q/Q extremal = 0, 0.01, 0.5, 0.99, 1 from left to right, respectively. 8 Since the effective potential in [22] is not symmetric, we need to consider the transformation of the master variable Φ 1 := r ∞ φ 1G , Φ 2 := φ 1E so that the effective potential is real symmetric. V 12 is given by multiplying r ∞ to Eq.…”

Revisiting the ADT mass of the five-dimensional rotating black holes with squashed horizons

“…[11][12][13][14][15][16][17][18][19][20][21][22]. As a prominent one of them, these black holes have provided opportunities to test several approaches on conserved quantities for various gravity theories, such as the Komar integral, the ADM formalism, the counterterm subtraction method, the (off-shell generalised) Abbott-DeserTekin (ADT) formulation and so on [2][3][4]8,[23][24][25][26][27][28][29][30][31].…”