Article

# Charged Rotating Kaluza-Klein Black Holes in Five Dimensions

Physical review D: Particles and fields 01/2008; DOI: 10.1103/PHYSREVD.77.044040

Source: arXiv

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**ABSTRACT:**We obtain a class of slowly rotating charged Kaluza-Klein black hole solutions of the five-dimensional Einstein-Maxwell-dilaton theory with arbitrary dilaton coupling constant. At infinity, the spacetime is effectively four-dimensional. In the absence of the squashing function, our solution reduces to the five-dimensional asymptotically flat slowly rotating charged dilaton black hole solution with two equal angular momenta. We calculate the mass, the angular momentum and the gyromagnetic ratio of these rotating Kaluza-Klein dilaton black holes. It is shown that the dilaton field and the non-trivial asymptotic structure of the solutions modify the gyromagnetic ratio of the black holes. We also find that the gyromagnetic ratio crucially depends on the dilaton coupling constant, \alpha, and decreases with increasing \alpha for any size of the compact extra dimension. Comment: 15 pages, 1 figuresPhysical review D: Particles and fields 08/2009; - [Show abstract] [Hide abstract]

**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 $SU(2) \times U(1) \simeq U(2)$ 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. We show that the modes of $J = 0$ and $ K=0,\pm 2$ and the modes of $K = \pm (J + 2)$ are stable against small perturbations from the positivity of the effective potential. As for $J = 0, K=\pm 1$ 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 $J = 0, K=\pm 1$ modes in general is open issue. However, we can show the stability for $J = 0, K=\pm 1$ modes in maximally charged case where the effective potential are positive out side of the horizon. Comment: 31 pages, 10 figures, title changedClassical and Quantum Gravity 05/2010; · 3.56 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A new holographic duality named Kerr/CFT correspondence was recently proposed to derive the statistical entropy of four-dimensional extremal Kerr black holes via identifying the quantum states in the near-horizon region with those of two-dimensional conformal field theory living on the boundary. In this paper, we apply this method to investigate five-dimensional extremal Kerr and Cvetič–Youm black holes with squashed horizons in different coordinates and find that the near-horizon geometries are not affected by the squashing transformation. Our investigation shows that the microscopic entropies are in agreement with those given by Bekenstein–Hawking formula. In addition, we have also investigated thermodynamics of the general non-extremal Cvetič–Youm black holes with squashed horizons.Nuclear Physics B 11/2009; · 4.33 Impact Factor

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