Journal ArticleDOI
Globally stationary but locally static space-times: A gravitational analog of the Aharonov-Bohm effect
TLDR
In this article, it was shown that any static metric on a space-time manifold with nonvanishing first Betti number (R}_{1}$ is a family of solutions to the electromagnetic Aharonov-Bohm effect.Abstract:
It is well known that gravitational fields may be locally the same but globally distinct due to differences in the topology of their underlying manifolds. Globally stationary but locally static gravitational fields provide an example of gravitational fields which are locally the same but globally distinct in spite of the homeomorphism of their underlying manifolds. Any static metric on a space-time manifold with nonvanishing first Betti number ${R}_{1}$ is shown to generate an ${R}_{1}$-parameter family of such solutions. These fields are seen to provide a gravitational analog of the electromagnetic Aharonov-Bohm effect. The exterior field of a rotating infinite cylinder of matter is discussed as an exactly soluble example.read more
Citations
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Journal ArticleDOI
General relativity in electrical engineering
Ulf Leonhardt,Thomas G. Philbin +1 more
TL;DR: In this article, the authors show that general relativity provides the theoretical tools for designing devices made of metamaterials, such as perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect and electromagnetic analogues of the event horizon.
Journal ArticleDOI
Three dimensional black holes and cylindrical general relativity
TL;DR: In this article, a black string solution of the four dimensional Einstein-Hilbert action, S = 1 16πG ∫ d 4X −g (R−2Λ), in a cylindrical spacetime is found.
Journal ArticleDOI
Gravitational Lensing from a Spacetime Perspective
TL;DR: In this paper, the theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations, where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature, and the basic equations and relevant techniques for calculating the position, shape, and brightness of images in an arbitrary general-relativistic spacetime.
Posted Content
Transformation Optics and the Geometry of Light
Ulf Leonhardt,Thomas G. Philbin +1 more
TL;DR: In this paper, the relationship between optics and general relativity is discussed, expressed more precisely between geometrical ideas normally applied in general relativity and the propagation of light, or electromagnetic waves in general, in materials.
Book ChapterDOI
Transformation Optics and the Geometry of Light
Ulf Leonhardt,Thomas G. Philbin +1 more
TL;DR: In this article, the geometry of light and the concepts of transformation optics are described and connections between geometry and electromagnetism in media that is as consistent and elementary as possible.
References
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Journal ArticleDOI
Significance of Electromagnetic Potentials in the Quantum Theory
Yakir Aharonov,D. Bohm +1 more
TL;DR: In this article, it was shown that there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish.
Journal ArticleDOI
Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields
Tai Tsun Wu,Chen Ning Yang +1 more
TL;DR: In this paper, an intrinsic and complete description of electromagnetism in a space-time region is formulated in terms of a nonintegrable phase factor, and connections on principal fiber bundles are identified.
Journal ArticleDOI
Classical physics as geometry
TL;DR: In this paper, the electromagnetic field is given by the Maxwell square root of the contracted curvature tensor tensor of Ricci and Einstein, and a detailed description in terms of the existing beautiful and highly developed mathematics of topology and harmonic vector fields is traced out in detail.
Journal ArticleDOI
IX.—The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry
TL;DR: The generalisation to the stationary case of the solution given by Weyl (1918) of Einstein's gravitational equations in a statical axially symmetric universe, has been attempted by various writers as mentioned in this paper.