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# The procedure for designing an electromagnetic cloaking device.

Source publication

In light of the surge in popularity of electromagnetic cloaking devices, we consider whether it is possible to use general relativity to cloak a volume of spacetime through gravitational lensing. We explore the cloaking properties of a spacetime through a ray-tracing procedure, wherein we plot the spatial trajectories of a congruence of initially p...

## Context in source publication

**Context 1**

... engineering systems with exotic electro- magnetic properties becomes a matter of searching for desirable coordinate transformations of flat space [1]. For example, consider the procedure for designing Schurig et al 's cloaking device (see Fig.(1)). We begin with a flat 2-dimensional space, and we draw a circle. ...

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## Citations

... Within the context of standard general relativity, there has now been over 33 years of serious theoretical work on the possibility of "traversable wormholes" [1][2][3][4][5], 29 years of recent work on "time machines" [6][7][8][9][10][11][12] and over 27 years of work on the theoretical possibility of "warp drives" [13][14][15][16][17][18]. These analyses, and their subsequent refinements, are based on "reverse engineering" the space-time metric to encapsulate some potentially interesting physics, and then using the Einstein equations to deduce what the stress-energy tensor must be to support these space-times [1,5,19,20]. ...

The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these into the Einstein equations. This latter approach has found frequent use when confronted with creative input from fiction, wormholes and warp drives being the most famous examples. In this paper, we again take inspiration from fiction and see what general relativity can tell us about the possibility of a gravitationally induced tractor beam. We base our construction on warp drives and show how versatile this ansatz alone proves to be. Not only can we easily find tractor beams (attracting objects), but repulsor/pressor beams are just as attainable, and a generalization to “stressor” beams is seen to present itself quite naturally. We show that all of these metrics would violate various energy conditions. This provides an opportunity to ruminate on the meaning of energy conditions as such and what we can learn about whether an arbitrarily advanced civilization might have access to such beams.

... The structures may be static, as in the case of spherical wormholes; contracting, as in the case of matter accretion shells around black holes [15] and shells collapsing into wormholes [16,17]; rotating and collapsing [18,19]; or expanding, as in the case of cosmic brane worlds [20], inflationary bubbles or bubble universes [21]. Such shells may split the universe into two domains, an interior and exterior joined by an infinitesimally thin wall of singular mass or pressure [22][23][24][25][26]; or into three domains [27], where the wall of finite thickness is sometimes called the transient layer [28]. Various interior and exterior metrics are assumed, including the Friedman-Robertson-Walker [29,30], Schwarzschild, de Sitter [31], anti-de Sitter [32], Minkowski, and Reissner-Nordstrom [33,34] metrics. ...

... The factor 1/2 in the first term on the right does not appear in some presentations of MOND, where different interpolating functions apply and where the potential covers all space [66]. However, since the second term increases with r and becomes dominant near R m , we can neglect the first term and construct an effective metric for the deep MOND region [67] g 00 1 + 2 ≅ φ m /c 2 1 + (2GM/c ≅ 2 R m ) ln (r/R m ), (22) which is accurate in the domain nR m <r<<R, for n a small integer on the order of 4 or 5. Note that g 00 >∞ ─ as r >∞. ...

Interest in general relativistic treatments of thin matter shells has flourished over recent decades, most notably in connection with astrophysical and cosmological applications such as black hole matter accretion, spherical wormholes, bubble universes, and cosmic domain walls. In the present paper, an asymptotically exact solution to Einstein's field equations for static ultra-thin spherical shells is derived using a continuous matter density distribution (r) ρ defined over all space. The matter density is modeled as a product of surface density μ 0 and a continuous or broadened spherical delta function. Continuity over the full domain 0<r<∞ ensures unambiguous determination of both the metric and coordinates across the shell wall, obviating the need to patch interior and exterior solutions using junction conditions. A unique change of variable allows integration with asymptotic precision. It is found that ultra-thin shells smaller than the Schwarzschild radius can be used to model supermassive black holes believed to lie at the centers of galaxies, possibly accounting for the flattening of the galactic rotation curve as described by Modified Newtonian Dynamics (MOND). Concentric ultra-thin shells may also be used for discrete sampling of arbitrary spherical mass distributions with applications in cosmology. Ultra-thin shells are shown to exhibit constant interior time dilation. The exterior solution matches the Schwarzschild metric. General black shell horizons, and singularities are also discussed.

... Several theoretical cloaking schemes had been proposed [2,3], which were quickly followed by experimental demonstrations in various portions of electromagnetic spectrum [4][5][6]. This body of work, which was done using various engineered effective metrics in "virtual" electromagnetic space-time, has inspired an effort to determine if gravitational cloaking can be achieved as a result of the gravitational curvature of physical space-time [7]. If possible, such gravitational cloaking would potentially shed a new light on the issue of dark matter in the Universe. ...

... Unfortunately, it appears that full three-dimensional gravitational cloaking requires exotic matter and energy sources [7], which makes it physically unrealizable. While this conclusion probably holds true in the threedimensional case, recent advances in cloaking technology led to the development of several simplified cloaking schemes. ...

Three-dimensional gravitational cloaking is known to require exotic matter and energy sources, which makes it arguably physically unrealizable. On the other hand, typical astronomical observations are performed using one-dimensional paraxial line of sight geometries. We demonstrate that unidirectional line of sight gravitational cloaking does not require exotic matter, and it may occur in multiple natural astronomical scenarios that involve gravitational lensing. In particular, recently discovered double gravitational lens SDSSJ0946+1006 together with the Milky Way appear to form a natural paraxial cloak. A natural question to ask, then, is how much matter in the Universe may be hidden from view by such natural gravitational cloaks? It is estimated that the total volume hidden from an observer by gravitational cloaking may reach about 1% of the total volume of the visible Universe.

... Therefore, it became possible to create metamaterials that simulate general relativity models and cosmological effects [14]. In particular, by choosing the correct transformation, or by direct use of the general metric, it is possible to simulate light propagating around a Schwarzschild black hole [15][16][17][18], to observe Hawking radiation [19], to simulate a spinning cosmic string [20], optical wormholes [21], gravitational lensing [22][23][24], de Sitter spacetime [25], Big Crunch [26], time travel [27]; all of these applications in the context of optics. ...

... The short answer is that it is very easy to make a spacetime which is curved so that a very large volume sits inside a very small box. You can even use curved spacetime geometries to make very large objects appear very very small [11]! Long story short: Bigger on the inside is too easy to bother. ...

... A person travelling within the TARDIS would describe it as a room which is constantly accelerating forwards. Furthermore, any events which occur inside of the TARDIS bubble must satisfy Novikov's self consistency condition 11 . ...

... Amy will only ever see the hands of her own clock move in a clockwise direction. When she looks out at Barbara, she will see the hands of Barbara's clock moving clockwise at some times and counterclockwise 11 the Doctor and Romana were stuck in a loop of repeating events in the "Megalos." The episode also involved a cactus as the villain, so... at others, depending on where Amy is along her circular trajectory. ...

This white paper is an explanation of Ben and Dave's TARDIS time machine,
written for laypeople who are interested in time travel, but have no technical
knowledge of Einstein's Theory of General Relativity.
The first part of this paper is an introduction to the pertinent ideas from
Einstein's theory of curved spacetime, followed by a review of other popular
time machine spacetimes. We begin with an introduction to curvature and
lightcones. We then explain the Alcubierre Warp Drive, the Morris-Thorne
wormhole, and the Tipler cylinder.
We then describe the Traversable Achronal Retrograde Domain in Spacetime
(TARDIS), and explain some of its general properties. Our TARDIS is a bubble of
spacetime curvature which travels along a closed loop in space and time. A
person travelling within the bubble will feel a constant acceleration. A person
outside of the TARDIS will see two bubbles: one which is evolving forwards in
time, and one which is evolving backwards in time. We then discuss the physical
limitations which may prevent us from ever constructing a TARDIS.
Finally, we discuss the method through which a TARDIS can be used to travel
between arbitrary points in space and time, and the possible dangers involved
with exiting a TARDIS from the wrong side.
Before we begin, would you like a Jelly Baby?

... It is worth mentioning, before we conclude this discussion, that many fascinating spacetime geometries require similar types of exotic matter. The list includes traversable wormholes (and thus time machines [6]), warp drives [1], and spacetime cloaking devices [9]. Speaking very broadly, only a civilization which has the capacity to travel through the universe at superluminal speeds would have the capacity to build Johansen's bubble. ...

In 1928, the late Francis Wayland Thurston published a scandalous manuscript
in purport of warning the world of a global conspiracy of occultists. Among the
documents he gathered to support his thesis was the personal account of a
sailor by the name of Gustaf Johansen, describing an encounter with an
extraordinary island. Johansen`s descriptions of his adventures upon the island
are fantastic, and are often considered the most enigmatic (and therefore the
highlight) of Thurston`s collection of documents.
We contend that all of the credible phenomena which Johansen described may be
explained as being the observable consequences of a localized bubble of
spacetime curvature. Many of his most incomprehensible statements (involving
the geometry of the architecture, and variability of the location of the
horizon) can therefore be said to have a unified underlying cause.
We propose a simplified example of such a geometry, and show using numerical
computation that Johansen`s descriptions were, for the most part, not simply
the ravings of a lunatic. Rather, they are the nontechnical observations of an
intelligent man who did not understand how to describe what he was seeing.
Conversely, it seems to us improbable that Johansen should have unwittingly
given such a precise description of the consequences of spacetime curvature, if
the details of this story were merely the dregs of some half remembered fever
dream.
We calculate the type of matter which would be required to generate such
exotic spacetime curvature. Unfortunately, we determine that the required
matter is quite unphysical, and possess a nature which is entirely alien to all
of the experiences of human science. Indeed, any civilization with mastery over
such matter would be able to construct warp drives, cloaking devices, and other
exotic geometries required to conveniently travel through the cosmos.

Interest in general relativistic treatments of thin matter shells has flourished over recent decades, most notably in connection with astrophysical and cosmological applications such as black hole matter accretion, spherical wormholes, bubble universes, and cosmic domain walls. In the present paper, an asymptotically exact solution to Einstein's field equations for static ultra-thin spherical shells is derived using a continuous matter density distribution (r) ρ defined over all space. The matter density is modeled as a product of surface density μ 0 and a continuous or broadened spherical delta function. Continuity over the full domain 0<r<∞ ensures unambiguous determination of both the metric and coordinates across the shell wall, obviating the need to patch interior and exterior solutions using junction conditions. A unique change of variable allows integration with asymptotic precision. It is found that ultra-thin shells smaller than the Schwarzschild radius can be used to model supermassive black holes believed to lie at the centers of galaxies, possibly accounting for the flattening of the galactic rotation curve as described by Modified Newtonian Dynamics (MOND). Concentric ultra-thin shells may also be used for discrete sampling of arbitrary spherical mass distributions with applications in cosmology. Ultra-thin shells are shown to exhibit constant interior time dilation. The exterior solution matches the Schwarzschild metric. General black shell horizons, and singularities are also discussed.

We propose a simple singularity-free coordinate transformation that could be implemented in Maxwell's equations in order to simulate one aspect of a Kerr black hole. Kerr black holes are known to force light to rotate in a predetermined direction inside the ergoregion. By making use of cosmological analogies and the theoretical framework of transformation optics, we have designed a metamaterial that can make light behave as if it is propagating around a rotating cosmological massive body. We present numerical simulations involving incident Gaussian beams interacting with the materials to verify our predictions. The ergoregion is defined through the dispersion curve of the off-axis permittivities components.