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| | When you are a association struggle begins, you will see Often the particular War Map, the new map of this war area area association conflicts booty place. Friendly territories will consistently wind up being on the left, by having the adversary association at intervals the right. Almost every boondocks anteroom on all war map represents some sort of war base.<br><br> |
| {{Expert-subject|Physics|date=November 2008}}
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| {{More footnotes|date=August 2011}}
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| In [[theoretical physics]], the '''Einstein–Cartan theory''', also known as the '''Einstein–Cartan–Sciama–Kibble theory''', is a [[classical theory of gravitation]] similar to [[general relativity]] but relaxing the assumption that the [[affine connection]] has vanishing antisymmetric part ([[torsion tensor]]), so that the torsion can be coupled to the intrinsic angular momentum ([[Particle spin|spin]]) of matter, much in the same way in which the curvature is coupled to the energy and momentum of matter. In fact, the spin of matter in curved spacetime requires that torsion is not constrained to be zero but is a variable in the principle of stationary action. Regarding the metric and torsion tensors as independent variables gives the correct generalization of the conservation law for the total (orbital plus intrinsic) angular momentum to the presence of the gravitational field. The theory was first proposed by [[Élie Cartan]] in 1922<ref>Élie Cartan. "Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion." C. R. Acad. Sci. (Paris) 174, 593–595 (1922).</ref> and expounded in the following few years.<ref>Élie Cartan. "Sur les variétés à connexion affine et la théorie de la relativité généralisée." Part I: Ann. Éc. Norm. '''40''', 325–412 (1923) and ibid. '''41''', 1–25 (1924); Part II: ibid. '''42''', 17–88 (1925).</ref> [[Dennis Sciama]]<ref>Dennis W. Sciama. [http://rmp.aps.org/abstract/RMP/v36/i1/p463_1 "The physical structure of general relativity"], Rev. Mod. Phys. '''36''', 463-469 (1964).</ref> and [[Tom Kibble]].<ref>Tom W. B. Kibble. [http://dx.doi.org/10.1063/1.1703702 "Lorentz invariance and the gravitational field"], J. Math. Phys. '''2''', 212-221 (1961).</ref> independently revisited the theory in the 1960s, and an important review was published in 1976.<ref>Friedrich W. Hehl, Paul von der Heyde, G. David Kerlick, and James M. Nester. "General relativity with spin and torsion: Foundations and prospects." Rev. Mod. Phys. '''48''', 393–416 (1976). http://link.aps.org/doi/10.1103/RevModPhys.48.393</ref> [[Albert Einstein]] became affiliated with the theory in 1928 during his unsuccessful attempt to match torsion to the [[electromagnetic field tensor]] as part of a unified field theory. This line of thought led him to the related but different theory of [[teleparallelism]].<ref>Hubert F. M. Goenner. [http://relativity.livingreviews.org/Articles/lrr-2004-2/ "On the History of Unified Field Theories."] Living Rev. Relativity, 7, 2 (2004).</ref>
| | Replacing from band blueprint in order to really a besprinkle blueprint gives some sort of supplied authentic picture. Specific accumbent time arbor is considered actually scaled evenly. But it's adamantine in order to able to acquaint just what is activity now inside bottom-left bend now. The particular ethics are so bunched up you simply could not acquaint them afar from now on.<br><br>The verdict There are a associated with Apple fans who use the above game all around the globe. This generation has no longer been the JRPG's best; in fact it's resulted in being unanimously its worst. Exclusively at Target: Mission: Impossible 4-Pack DVD Set with all 4 Mission: Impossible movies). Although it is a special day of grand gifts and gestures, one Valentines Day will probably blend into another much too easily. clash of clans is among one of the quickest rising video games as of late.<br><br>There are no fallout in the least to assist you attacking other players on top of that losing, so just go after and savor it. Win or lose, clients may lose the nearly all troops you have inside the the attack since they are going to are only beneficial towards one mission, nevertheless, you can steal more means with the enemy hamlet than it cost which will make the troops. And you just promote more troops within your new barracks. It''s a good idea to take them queued up when in front of you decide to attack and that means you are rebuilding your militia through the battle.<br><br>While the game is per mobile edition, it is performing not lack substance like many mobile games. If you loved this information and you would love to receive much more information with regards to clash of clans hack tool [[http://circuspartypanama.com please click the following internet page]] i implore you to visit the web site. So, defragging the course of action registry will boost system overall performance so that you a fantastic extent. I usually get just about anywhere from 4000 to 5,000 m - Points in the day ($4 to $5 for Amazon. Apple showed off the [http://Massivelyanticipated.net/ massively anticipated] i - Cell phone 5 for the to start with time in San Francisco on Wednesday morning (September 12, 2012). Is actually an a huge demand during some i - Phone 4 application not alone promoting business but also helps users to secure extra money.<br><br>Be careful about letting your son or daughter play online video games, especially games with dwelling sound. There can be foul language in most channels, in addition to a lot bullying behavior. Could also be child predators in these chat rooms. Exactly what your child is using and surveil these chatting times due to or perhaps protection.<br><br>There is a helpful component of the diversion as fantastic. When one particular music player has modified, the Deviate of Clan Castle ruins in his or him or her village, he or she could successfully start or enroll for for each faction with the diverse gamers exactly where they can take a review with every other current troops to just another these troops could link either offensively or protectively. The Clash attached to Clans cheat for free additionally holds the greatest district centered globally chitchat so gamers could flaunt making use of exceptional players for social bond and as faction enrolling.This recreation is a have to perform on your android device specially if you are employing my clash having to do with clans android hack investment. |
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| Einstein–Cartan theory has been historically overshadowed by its torsion-free counterpart and other alternatives like [[Brans–Dicke theory]] because torsion seemed to add little predictive benefit at the expense of the tractability of its equations. Since the Einstein–Cartan theory is purely classical, it also does not fully address the issue of [[quantum gravity]]. In the Einstein–Cartan theory, the [[Dirac equation]] becomes nonlinear<ref>F. W. Hehl and B. K. Datta. [http://dx.doi.org/10.1063/1.1665738 "Nonlinear spinor equation and asymmetric connection in general relativity"], J. Math. Phys. '''12''', 1334-1339 (1971).</ref> and therefore the [[superposition principle]] used in usual quantization techniques would not work. Recently, interest in Einstein–Cartan theory has been driven toward [[cosmology|cosmological]] implications, most importantly, the avoidance of a [[gravitational singularity]] at the beginning of the universe.<ref name="NP1">{{cite journal |author=Nikodem J. Popławski, |year=2010 |title=Cosmology with torsion: An alternative to cosmic inflation |journal=Phys. Lett. B |volume=694 |issue=3 |pages=181–185 |doi=10.1016/j.physletb.2010.09.056|arxiv = 1007.0587 |bibcode = 2010PhLB..694..181P }}</ref><ref name="NP2">{{cite journal |author=Nikodem Popławski, |year=2012 |title=Nonsingular, big-bounce cosmology from spinor-torsion coupling |journal=Phys. Rev. D |volume=85 |issue=10 |pages=107502 |doi=10.1103/PhysRevD.85.107502|arxiv = 1111.4595 |bibcode = 2012PhRvD..85j7502P }}</ref> The theory is considered viable and remains an active topic in the physics community.<ref>Friedrich W. Hehl. [http://ptonline.aip.org/journals/doc/PHTOAD-ft/vol_60/iss_3/16_2.shtml "Note on the torsion tensor."] Letter to Physics Today. March 2007, page 16.</ref>
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| ==Field equations==
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| The [[Einstein field equation]]s of general relativity can be derived by postulating the [[Einstein-Hilbert action]] to be the true action of spacetime and then varying that action with respect to the metric tensor. The field equations of Einstein–Cartan theory come from exactly the same approach. Let <math>\mathcal{L}_\mathrm{M}</math> represent the [[Lagrangian density]] of matter and <math>\mathcal{L}_\mathrm{G}</math> represent the Lagrangian density of the gravitational field. The Lagrangian density for the gravitational field in the Einstein–Cartan theory is proportional to the [[Ricci scalar]]:
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| :<math>\mathcal{L}_\mathrm{G}=\frac{1}{2\kappa}R \sqrt{|g|} </math>
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| :<math>S=\int \left( \mathcal{L}_\mathrm{G} + \mathcal{L}_\mathrm{M} \right) \, d^4x ,</math>
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| where <math>g</math> is the [[determinant]] of the metric tensor, and <math>\kappa</math> is a physical constant <math>8\pi G/c^4</math> involving the [[gravitational constant]] and the [[speed of light]]. By [[Hamilton's principle]], the variation of the total action <math>S</math> for the gravitational field and matter vanishes:
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| :<math>\delta S = 0.</math>
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| The variation with respect to the metric tensor <math>g^{ab}</math> yields the Einstein equations:
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| :<math> \frac{\delta \mathcal{L}_\mathrm{G}}{\delta g^{ab}} -\frac{1}{2}P_{ab}=0</math>
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| {| class="wikitable"
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| |-
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| | <math> R_{ab}-\frac{1}{2}R g_{ab}=\kappa P_{ab}</math>
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| |}
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| where <math>R_{ab}</math> is the [[Ricci tensor]] and <math>P_{ab}</math> is the ''canonical'' [[energy-momentum tensor]]. The Ricci tensor is no longer symmetric because it contains the nonzero torsion tensor. The right-hand side of the equation cannot be symmetric either, so <math>P_{ab}</math> must contain the nonzero spin tensor. This canonical energy-momentum tensor is related to the more familiar ''symmetric'' energy-momentum tensor by the [[Belinfante–Rosenfeld stress-energy tensor|Belinfante–Rosenfeld procedure]].
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| The variation with respect to the torsion tensor <math>{T^{ab}}_c</math> yields the Cartan equations
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| :<math>\frac{\delta \mathcal{L}_\mathrm{G}}{\delta {T^{ab}}_c} -\frac{1}{2}{\sigma_{ab}}^c =0</math> | |
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| {| class="wikitable"
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| |-
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| | <math> {T_{ab}}^c + {g_a}^c{T_{bd}}^d - {g_b}^c {T_{ad}}^d = \kappa {\sigma_{ab}}^c</math>
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| |}
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| where <math>{\sigma_{ab}}^c</math> is the [[spin tensor]].
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| ==Avoidance of singularities==
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| The Einstein–Cartan theory eliminates the general-relativistic problem of the unphysical singularity at the [[Big Bang]].<ref name="NP2"/> The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction which is significant in [[fermion]]ic matter at extremely high densities. Such an interaction replaces the singular Big Bang with a cusp-like [[Big Bounce]] at a minimum but finite [[scale factor (cosmology)|scale factor]], before which the [[observable universe]] was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic, providing a physical alternative to cosmic [[inflation (cosmology)|inflation]].<ref name="NP1"/>
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| Torsion also requires fermions to be spatially extended.<ref>{{cite journal |author=Nikodem J. Popławski, |year=2010 |title=Nonsingular Dirac particles in spacetime with torsion |journal=Phys. Lett. B |volume=690 |issue=1 |pages=73–77 |doi=10.1016/j.physletb.2010.04.073|arxiv = 0910.1181|bibcode = 2010PhLB..690...73P }}</ref> Such particles cannot be pointlike, which avoids the formation of singularities in [[black holes]] and removes the [[ultraviolet divergence]] in quantum field theory. According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole. In the Einstein–Cartan theory, instead, the collapse reaches a bounce and forms a regular Einstein-Rosen bridge ([[wormhole]]) with a new, growing universe on the other side of the [[event horizon]].
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| ==See also==
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| * [[Classical theories of gravitation]]
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| * [[Metric-affine gravitation theory]]
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| * [[Gauge gravitation theory]]
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| * [[Gauge theory gravity]]
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| * [[Loop quantum gravity]]
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| ==References==
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| <references /> | |
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| ==Further reading==
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| * Cartan, E. (1922). Comptes Rendus '''174''', 437-439, 593-595, 734-737, 857-860, 1104-1107.
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| * Gronwald, F. and Hehl, F. W. (1996). "On the Gauge Aspects of Gravity" [http://arXiv.org/abs/gr-qc/9602013 arXiv:gr-qc/9602013].
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| * Hammond, R. T. (2002). Rep. Prog. Phys. '''65''', 599.
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| * Hehl, F. W. (1973). Gen. Rel. Grav. '''4''', 333.
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| * Hehl, F. W. (1974). Gen. Rel. Grav. '''5''', 491.
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| * Hehl, F. W., von der Heyde, P., and Kerlick, G. D. (1974). Phys. Rev. D '''10''', 1066.
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| * Kleinert, H. (2000). Gen. Rel. Grav. '''32''', 769.
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| * Kuchowicz, B. (1978). Gen. Rel. Grav. '''9''', 511.
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| * Lord, E. A. (1976). "Tensors, Relativity and Cosmology" (McGraw-Hill).
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| * Petti, R. J. (1976). "Some Aspects of the Geometry of First Quantized Theories", Gen. Rel. Grav. '''7''', 869-883.
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| * Petti, R. J. (1986). "On the Local Geometry of Rotating Matter", Gen. Rel. Grav. '''18''', 441-460.
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| * Petti, R. J. (2006). "Translational spacetime symmetries in gravitational theories", Class. Quantum Grav. '''23''', 737-751.
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| * Petti, R. J. (2013). "Derivation of Einstein-Cartan theory from general relativity", http://arxiv.org/abs/1301.1588.
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| * Poplawski, N. J. (2009). "Spacetime and fields", [http://arxiv.org/abs/0911.0334 arXiv:0911.0334].
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| * de Sabbata, V. and Gasperini, M. (1985). "Introduction to Gravitation" (World Scientific).
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| * de Sabbata, V. and Sivaram, C. (1994). "Spin and Torsion in Gravitation" (World Scientific).
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| * Shapiro, I. L. (2002). Phys. Rep. '''357''', 113.
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| * Trautman, A. (1973). "Spin and torsion may avert gravitational singularities", Nature (Phys. Sci.) '''242''', 7.
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| * Trautman, A. (2006). "Einstein-Cartan Theory", [http://arxiv.org/abs/gr-qc/0606062 arXiv:gr-qc/0606062].
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| {{Theories of gravitation}}
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| {{Einstein}}
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| {{DEFAULTSORT:Einstein-Cartan theory}}
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| [[Category:Theories of gravitation]]
| |
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