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, s
quashed 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.
We construct asymptotically Kaluza-Klein solutions in five-dimensional Einstein-Maxwell theory which represent a pair of extremal, charged, static black holes on Kerr-Taub-bolt space. Regularity conditions require that the topology of spatial infinit
y and that of each black hole are not S$^3$, but different lens spaces. We show that for a given topology at spatial infinity, there are an infinite number of different horizon topologies for the black hole pair. We briefly discuss a generalization to the case with a positive cosmological constant.
The geodesic equation in the five-dimensional singly rotating black ring is non-integrable unlike the case of the Myers-Perry black hole. In the Newtonian limit of the black ring, its geodesic equation agrees with the equation of motion of a particle
in the Newtonian potential due to a homogeneous ring gravitational source. In this paper, we show that the Newtonian equation of motion allows the separation of variables in the spheroidal coordinates, providing an non-trivial constant of motion quadratic in momenta. This shows that the Newtonian limit of a black ring recovers the symmetry of its geodesic system, and the geodesic chaos is caused by relativistic effects.
We study the dynamics of the Nambu-Goto membranes with cohomogeneity one symmetry, i.e., the membranes whose trajectories are foliated by homogeneous surfaces. It is shown that the equation of motion reduces to a geodesic equation on a certain manifo
ld, which is constructed from the original spacetime and Killing vector fields thereon. A general method is presented for classifying the symmetry of cohomogeneity one membranes in a given spacetime. The classification is completely carried out in Minkowski spacetime. We analyze one of the obtained classes in depth and derive an exact solution.
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.
We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of R
iemann tensor diverge at the horizon in the coordinates of the $C^1$ extension. In particular, the divergence of a component of the Riemann tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza-Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
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 re
gularity 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.
We explore equilibrium solutions of non-topological solitons in a general class of scalar field theories which include global U(1) symmetry. We find new types of solutions, tube-shaped and crust-shaped objects, and investigate their stability. Like Q
-balls, the new solitons can exist in supersymmetric extensions of the Standard Model, which may responsible for baryon asymmetry and dark matter. Therefore, observational signals of the new solitons would give us more informations on the early universe and supersymmetric theories.
It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole spacetime: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to
see how an electric current affects the Meissner-like effect, we study a force-free electromagnetic system in a static and spherically symmetric extreme black hole spacetime. By assuming that the rotational angular velocity of the magnetic field is very small, we construct a perturbative solution for the Grad-Shafranov equation, which is the basic equation to determine a stationary, axisymmetric electromagnetic field with a force-free electric current. Our perturbation analysis reveals that, if an electric current exists, higher multipole components may be superposed upon the monopole component on the event horizon, even if the black hole is extreme.
