Five-dimensional Einstein-Maxwell Theory Research Articles

Quasinormal Modes of a Charged Black Hole with Scalar Hair

Based on the five-dimensional Einstein–Maxwell theory, Bah et al. constructed a singularity-free topology star/black hole [Phys. Rev. Lett. 126, 151101 (2021)]. After performing the Kaluza–Klein reduction, i.e., integrating the extra space dimension, it can obtain an effective four-dimensional spherically static charged black hole with scalar hair. In this paper, we study the quasinormal modes (QNMs) of the scalar, electromagnetic, and gravitational fields in the background of this effective four-dimensional charged black hole. The radial parts of the perturbed fields all satisfy a Schrödinger-like equation. Using the asymptotic iteration method, we obtain the QNM frequencies semianalytically. For low-overtone QNMs, the results obtained using both the asymptotic iteration method and the Wentzel–Kramers–Brillouin approximation method agree well. In the null coordinates, the evolution of a Gaussian package is also studied. The QNM frequencies obtained by fitting the evolution data also agree well with the results obtained using the asymptotic iteration method.

Topological Stars and Black Holes.

We study smooth bubble spacetimes in five-dimensional Einstein-Maxwell theory that resemble four-dimensional magnetic black holes upon Kaluza-Klein reduction. We denote them as topological stars since they have topological cycles supported by magnetic flux. They can be macroscopically large compared to the size of the Kaluza-Klein circle and could describe qualitative properties of microstate geometries for astrophysical black holes. We also describe five-dimensional black strings without curvature singularity, the interior caps as a two-dimensional Milne space with a bubble.

Charged black strings in a five-dimensional Kasner universe

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.

A pair of extremal charged black holes on Kerr–Taub-bolt space

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 infinity and that of each black hole are not S3, 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.

A no black hole theorem

We show that one cannot put a stationary (extended) black hole inside certain gravitating flux-tubes. This includes an electric flux-tube in five-dimensional Einstein–Maxwell theory, as well as the standard flux-branes of string theory. The flux always causes the black hole to grow indefinitely. One finds a similar restriction in a Kaluza–Klein setting where the higher dimensional spacetime contains no matter.

Charged black holes in a five-dimensional Kaluza-Klein universe

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.

Charged rotating Kaluza-Klein multiblack holes and multiblack strings in five-dimensional Einstein-Maxwell theory

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.

Fluid/gravity correspondence, local Wald entropy current and gravitational anomaly

We propose, in the framework of the fluid/gravity correspondence, a definition for a local horizon entropy current for higher-curvature gravitational theories. The current is well-defined to first order in fluid gradients for general gravity actions with an algebraic dependence on the Riemann tensor. As a detailed example, we consider five-dimensional Einstein-Maxwell theory with a mixed gauge-gravitational Chern-Simons term. In this theory, we construct the proposed entropy current on a charged black-brane background, and show that it has a non-negative divergence. Moreover, a complete correspondence between the charged black-brane horizon's dynamics and the hydrodynamics of an anomalous four-dimensional field theory is established. Our proposed entropy current is then found to coincide with the entropy current of the anomalous field theory fluid.

Instability by Chern-Simons and/or transgressions

It was demonstrated recently that there is an upper bound of the Chern-Simons coupling of the five-dimensional Einstein-Maxwell theory, beyond which the electrically charged AdS2 × S 3 vacuum solution becomes unstable. We generalize the result to a general class of gravity theories involving Chern-Simons and/ or transgression terms and find their upper bounds for stability. We show that supergravities with AdS×Sphere vacua satisfy the bounds.

Static near-horizon geometries in five dimensions

We consider the classification of static near-horizon geometries of stationary extremal (not necessarily BPS) black hole solutions of five-dimensional Einstein–Maxwell theory coupled to a Chern–Simons term with coupling ξ (with ξ = 1 corresponding to supergravity). Assuming that the black holes have two rotational symmetries, we show that their near-horizon geometries are either the direct product AdS3 × S2 or a warped product of AdS2 and compact 3D space. In the AdS2 case we are able to classify all possible near-horizon geometries with no magnetic fields. There are two such solutions: the direct product AdS2 × S3 as well as a warped product of AdS2 and an inhomogeneous S3. The latter solution turns out to be a near-horizon limit of an extremal Reissner–Nordström black hole in an external electric field. In the AdS2 case with magnetic fields, we reduce the problem (in all cases) to a single nonlinear ODE. We show that if there are any purely magnetic solutions of this kind, they must have S1 × S2 horizon topology, and for ξ2 < 1/4 we find examples of solutions with both electric and magnetic fields.

Atiyah-Hitchin space in five-dimensional Einstein-Maxwell theory

We construct exact solutions to five-dimensional Einstein-Maxwell theory based on Atiyah-Hitchin space. The solutions cannot be written explicitly in a closed form, so their properties are investigated numerically. The five-dimensional metric is regular everywhere except on the location of original bolt in four-dimensional Atiyah-Hitchin base space. On each time-fixed slices, the metric, asymptotically approaches an Euclidean Taub-NUT space.

Charged rotating Kaluza-Klein black holes in five dimensions

We construct a new charged rotating Kaluza-Klein black hole solution in the five-dimensional Einstein-Maxwell theory with a Chern-Simon term. The features of the solutions are also investigated. The spacetime is asymptotically locally flat, i.e., it asymptotes to a twisted S{sup 1} bundle over the four-dimensional Minkowski spacetime. The solution describe a non-BPS black hole rotating in the direction of the extra dimension. The solutions have the limits to the supersymmetric black hole solutions, a new extreme non-BPS black hole solution and a new rotating non-BPS black hole solution with a constant twisted S{sup 1} fiber.

Cosmological black holes on Taub–NUT space in five-dimensional Einstein–Maxwell theory

The cosmological black hole solution on the Gibbons–Hawking space has been constructed. We also investigate the properties of this solution in the case of a single-black hole. Unlike the Kastor–Traschen solution, which becomes a static solution in a single-black hole, this solution is not static even in a single-black hole case.

Kaluza–Klein multi-black holes in five-dimensional Einstein–Maxwell theory

We construct Kaluza–Klein multi-black hole solutions on the Gibbons–Hawking multi-instanton space in the five-dimensional Einstein–Maxwell theory. We study the geometric properties of the multi-black hole solutions. In particular, unlike the Gibbons–Hawking multi-instanton solutions, each nut-charge is able to take a different value due to the existence of a black hole on it. The spatial cross section of each horizon is admitted to have the topology of a different lens space in addition to S3.

Black holes on Eguchi-Hanson space in five-dimensional Einstein-Maxwell theory

We construct a pair of black holes on the Eguchi-Hanson space as a solution in the five-dimensional Einstein-Maxwell theory.

Kaluza-Klein Black Holes with Squashed Horizons

We study geometrical structures of charged static black holes in the five-dimensional Einstein-Maxwell theory. The black holes we study have horizons in the form of squashed $ {\rm S}^3$, and their asymptotic structure consists of a twisted ${\rm S}^1$ bundle over the four-dimensional flat spacetime at the spatial infinity. The spacetime we consider is fully five-dimensional in the vicinity of the black hole and four-dimensional with a compact extra dimension at infinity.