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Register a new userCharged Black Holes in a Five-dimensional Kaluza-Klein Universe
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We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes expanding three dimensions and shrinking an extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.
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We construct exact solutions, which represent regular charged rotating Kaluza-Klein multi-black holes in the five-dimensional pure Einstein-Maxwell theory. Quantization conditions between the mass, the angular momentum, and charges appear from the regularity condition of horizon. We also obtain multi-black string solutions by taking some limits in the solutions. We extend the black hole solutions to the five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling constant.
We investigate five-dimensional vacuum solutions which represent rotating multi-black holes in asymptotically Kaluza-Klein spacetimes. We show that multi-black holes rotate maximally along extra dimension, and stationary configurations in vacuum are achieved by the balance of the gravitational attraction force and repulsive force caused by the rotations of black holes. We also show that each black hole can have the different topology of the lens space in addition to the spherical topology, and mass of black holes are quantized by the size of extra dimension and horizon topology.
The newly proposed island formula for entanglement entropy of Hawking radiation is applied to spherically symmetric 4-dimensional eternal Kaluza-Klein (KK) black holes (BHs). The charge $Q$ of a KK BH quantifies its deviation from a Schwarzschild BH. The impact of $Q$ on the island is studied at both early and late times. The early size of the island, emph{if exists}, is of order Planck length $ell_{mathrm{P}}$, and will be shortened by $Q$ by a factor $1/sqrt2$ at most. The late-time island, whose boundary is on the outside but within a Planckian distance of the horizon, is slightly extended. While the no-island entropy grows linearly, the late-time entanglement entropy is given by island configuration with twice the Bekenstein-Hawking entropy. Thus we reproduce the Page curve for the eternal KK BHs. Compared with Schwarzschild results, the Page time and the scrambling time are marginally delayed. Moreover, the higher-dimensional generalization is presented. Skeptically, in both early and late times, there are Planck length scales involved, in which a semi-classical description of quantum fields breaks down.
We construct time-dependent charged black string solutions in five-dimensional Einstein-Maxwell theory. In the far region, the spacetime approaches a five-dimensional Kasner universe with a expanding three-dimensional space and a shrinking extra dimension. Near the event horizon, the spacetime is approximately static and has a smooth event horizon. We also study the motion of test particles around the black string and show the existence of quasi-circular orbits. Finally, we briefly discuss the stability of this spacetime.
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)times U(1)simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.
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