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Register a new userRotating Kaluza-Klein Multi-Black Holes with Godel Parameter
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We obtain new five-dimensional supersymmetric rotating multi-Kaluza-Klein black hole solutions with the Godel parameter in the Einstein-Maxwell system with a Chern-Simons term. These solutions have no closed timelike curve outside the black hole horizons. At the infinity, the space-time is effectively four-dimensional. Each horizon admits various lens space topologies L(n;1)=S^3/Z_n in addition to a round S^3. The space-time can have outer ergoregions disjointed from the black hole horizons, as well as inner ergoregions attached to each horizon. We discuss the rich structures of ergoregions.
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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.
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.
Applying squashing transformation to Kerr-Godel black hole solutions, we present a new type of a rotating Kaluza-Klein black hole solution to the five-dimensional Einstein-Maxwell theory with a Chern-Simon term. The new solutions generated via the squashing transformation have no closed timelike curve everywhere outside the black hole horizons. At the infinity, the metric asymptotically approaches a twisted S^1 bundle over a four-dimensional Minkowski space-time. One of the remarkable features is that the solution has two independent rotation parameters along an extra dimension associated with the black holes rotation and the Godels rotation. The space-time also admits the existence of two disconnected ergoregions, an inner ergoregion and an outer ergoregion. These two ergoregions can rotate in the opposite direction as well as in the same direction.
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