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{{Redirect|Warp factor|the concept in [[Star Trek]]|Warp drive (Star Trek)}}
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{{Multiple issues
| essay=July 2009
| refimprove=October 2010
}}
In [[physics]], '''Randall–Sundrum models''' (also called '''5-dimensional warped geometry theory''') imagines that the real world is a higher-dimensional universe described by [[warped geometry]]. More concretely, our universe is a five-dimensional [[anti-de Sitter space]] and the elementary particles except for the [[graviton]] are localized on a (3&nbsp;+&nbsp;1)-dimensional [[Membrane (M-Theory)|brane]] or branes.
 
The models were proposed in 1999 by [[Lisa Randall]] and [[Raman Sundrum]] because they were dissatisfied with the [[large extra dimension|universal extra-dimensional]] models then in vogue. Such models require two fine tunings; one for the value of the [[Brane cosmology|bulk]] [[cosmological constant]] and the other for the [[brane tension]]s. Later, while studying RS models in the context of the [[AdS/CFT correspondence]], they showed how it can be dual to [[Technicolor (physics)|technicolor model]]s.
 
There are two popular models. The first, called '''RS1''', has a finite size for the extra dimension with two branes, one at each end.  The second, '''RS2''', is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model.
 
==Overview==
The model is a [[braneworld]] theory developed while trying to solve the [[hierarchy problem]] of the [[Standard Model]]. It involves a finite five-dimensional [[Brane cosmology|bulk]] that is extremely warped and contains two [[branes]]: the Planckbrane (where gravity is a relatively strong force; also called "Gravitybrane") and the Tevbrane (our home with the Standard Model particles; also called "Weakbrane"). In this model, the two branes are separated in the not-necessarily large fifth dimension by approximately 16 units (the units based on the brane and bulk energies). The Planckbrane has positive brane energy, and the Tevbrane has negative brane energy. These energies are the cause of the extremely warped [[spacetime]].
 
==Graviton probability function==
In this warped spacetime that is ''only'' warped along the fifth dimension, the [[graviton]]'s [[probability function]] is extremely high at the Planckbrane, but it drops exponentially as it moves closer towards the Tevbrane. In this, gravity would be much weaker on the Tevbrane than on the Planckbrane.
 
==Growing, shrinking, and changing weight: solving the hierarchy problem==
Also in this model, any object moving from the Planckbrane to the Tevbrane in the bulk would be growing, becoming lighter, and moving more slowly through time. Distance and time expand near the Tevbrane, and mass and energy shrink near it. This creates an alternate explanation of gravity's weakness in the Tevbrane: everything is lighter. An interesting part of this is that the hierarchy problem is automatically solved. The main scale on the Planckbrane would be the [[Planck scale]]. However, the change by 16 units causes the scales to change by 16 orders of magnitude. On the Planckbrane, strings would be 10<sup>−33</sup> cm in size, but on the Tevbrane they'd be 10<sup>−17</sup> cm. In fact, this makes the mass scale for the Weakbrane based on about a TeV. Therefore, you no longer have the strange range of masses and energies. If this is the case, we should see evidence when the [[Large Hadron Collider]] begins working.
 
==The RS1 model==
The RS1 model attempts to address the [[hierarchy problem]].  The warping of the extra dimension is analogous to the warping of [[spacetime]] in the vicinity of a massive object, such as a [[black hole]].  This warping, or red-shifting, generates a large ratio of energy scales so that the natural energy scale at one end of the extra dimension is much larger than at the other end.
 
:<math>\mathrm{d}s^2={1\over k^2 y^2}(\mathrm{d}y^2+\eta_{\mu\nu}\,\mathrm{d}x^\mu\, \mathrm{d}x^\nu)</math>
 
where ''k'' is some constant and η has "-+++" [[metric signature]]. This space has [[Boundary (topology)|boundaries]] at ''y'' = 1/''k'' and ''y'' = 1/''Wk'', with <math>0\le {1 \over k} \le {1 \over Wk}</math> where ''k'' is around the [[Planck scale]] and ''W''  is the warp factor and ''Wk''  is around a [[TeV]]. The boundary at ''y'' = 1/''k'' is called the '''Planck brane''' and the boundary at ''y'' = 1/''Wk'' is called the '''TeV brane'''.  The particles of the [[standard model]] reside on the TeV brane. The distance between both branes is only &minus;ln(''W'')/''k'', though.
 
In another [[coordinate system]],
 
:<math>\varphi\ \stackrel{\mathrm{def}}{=}\  -{\pi \ln(ky)\over \ln(W)},</math>
 
so that
 
:<math>0\le \varphi \le \pi</math>
 
and
 
:<math>\mathrm{d}s^2=\left ({\ln(W)\over \pi k}\right )^2\, \mathrm{d}\varphi^2+e^{2\ln(W)\varphi\over \pi}\eta_{\mu\nu}\,\mathrm{d}x^\mu\, \mathrm{d}x^\nu.</math>
 
==The RS2 model==
The RS2 model uses the same geometry as RS1, but there is no TeV brane. The particles of the standard model are presumed to be on the Planck brane. This model was originally of interest because it represented an infinite 5-dimensional model which, in many respects, behaved as a 4-dimensional model. This setup may also be of interest for studies of the [[AdS/CFT]] conjecture.
 
==Prior models==
In 1998/99 Merab Gogberashvili published on [[arXiv]] a number of articles on a very similar theme.<ref>M. Gogberashvili, ''Hierarchy problem in the shell universe model'', [http://arxiv.org/abs/hep-ph/9812296 arXiv:hep-ph/9812296].</ref><ref>M. Gogberashvili, ''Our world as an expanding shell'', [http://arxiv.org/abs/hep-ph/9812365 arXiv:hep-ph/9812365].</ref><ref>M. Gogberashvili, ''Four dimensionality in noncompact Kaluza-Klein model'', [http://arxiv.org/abs/hep-ph/9904383 arXiv:hep-ph/9904383].</ref> In those papers he showed that if the Universe is considered as a thin shell (a mathematical [[synonym]] for "brane") expanding in 5-dimensional space then there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional [[cosmological constant]] and Universe thickness, and thus to solve the [[hierarchy problem]]. It was also shown that four-dimensionality of the Universe is the result of [[Stability theory|stability]] requirement since the extra component of the [[Einstein field equations]] giving the localized solution for [[matter]] fields coincides with the one of the conditions of stability.
 
==See also==
*[[Kaluza–Klein theory]]
*[[Large extra dimension|ADD model]]
*[[DGP model]]
 
==References==
{{Reflist}}
 
==Further reading==
*{{cite journal
|last=Randall |first=Lisa |coauthors=Sundrum, Raman
|year=1999
|title=Large Mass Hierarchy from a Small Extra Dimension
|journal=[[Physical Review Letters]]
|volume=83 |issue=17 |pages=3370&ndash;3373
|doi=10.1103/PhysRevLett.83.3370 |bibcode=1999PhRvL..83.3370R
|arxiv = hep-ph/9905221 }}
*{{cite book
|last=Randall |first=Lisa
|year=2005
|title=Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions
|publisher=HarperCollins |location=New York
|isbn=0-06-053108-8
}}
 
==External links==
*[http://www.physics.harvard.edu/people/facpages/randall.html Lisa Randall's web page at Harvard University]
*[http://physics-astronomy.jhu.edu/people/faculty/sundrum.html Raman Sundrum's web page at Johns Hopkins University]
 
{{DEFAULTSORT:Randall-Sundrum Model}}
[[Category:Physical cosmology]]
[[Category:Particle physics]]
[[Category:String theory]]

Latest revision as of 03:52, 12 March 2014

For your very own offense, you might contain Gunboats which can basically shoot at enemy safeguarding coming from a range and Landing Work which you must refill when you train gadgets for example Rifleman, Heavy, Zooka, Warrior and Containers. To your village defenses, you might hold structures like Mortar, Washer Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Bomb Launcher to assist your family eradicate enemies.

These amend delivers a large amount of notable enhancements, arc of which could becoming the new Dynasty War Manner. In this specific mode, you can designed combating dynasties and lessen utter rewards aloft his or beat.

Many individuals which play clash of clans are looking for ways of getting fully free gems. The gallstones are very important when they give the player capabilities and the power increase their gaming experience. As opposed to added equivalent games in mobile or portable websites, especially those where individuals use various cracks in buy to get these practical information in relation to free, the nature involved with farmville and its format does not enable almost varieties of hacks that you can put to the game. Everyone is always looking for ways on how to get free gems present in clash of clans nonetheless most important thing to perform is to employ a great way to earn these consumers for free, save these kind of suitably and use these people where necessary.

Suppose you're playing a round online, and you range across another player who seem to seems to be disheartening other players (or you, in particular) intentionally, won't take it personally. This is called "Griefing," and it's the playing games equivalent of Internet trolling. Griefers are solely out for negative attention, and you give them all what they're looking about if you interact all of them. Don't get emotionally utilized in what's happening and even simply try to neglected.

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