View source for De Moivre's law

The '''R=T model''',<ref>
{{cite journal | last1        = Mann | first1       = Robert | authorlink1  = Robert B. Mann | last2        = Shiekh | first2       = A. | last3 = Tarasov | first3 = L. | date         = 3 Sep 1990 | title        = Classical and quantum properties of two-dimensional black holes | journal      = Nuclear Physics | volume       = 341 | issue        = 1 | series       = B | pages        = 134&ndash;154 | doi          = 10.1016/0550-3213(90)90265-F | url          = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47200F0-25W&_user=10&_coverDate=09/03/1990&_rdoc=7&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235531%231990%23996589998%23351258%23FLP%23display%23Volume)&_cdi=5531&_sort=d&_docanchor=&view=c&_ct=14&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a5aa7425ba25ffef424f5a4d2d0c680a&searchtype=a | archiveurl   = http://ccdb4fs.kek.jp/cgi-bin/img_index?8912298 | archivedate  = Dec 1989}}
</ref> also known as '''[[Roman Jackiw|Jackiw]]&ndash;[[Claudio Teitelboim|Teitelboim]] gravity''' is a theory of gravity with [[dilaton]] coupling in one spatial and one time dimension. It should not be confused<ref>{{cite journal | last1 = Grumiller | first1 = Daniel | authorlink1 = Daniel Grumiller | last2 = Kummer | first2 = Wolfgang | authorlink2 = Wolfgang Kummer | last3 = Vassilevich | first3 = Dmitri | authorlink3 = Dmitri Vassilevich | date = October 2002 | title = Dilaton Gravity in Two Dimensions | journal = Physics Reports | volume = 369 | issue = 4 | pages = 327&ndash;430 | doi = 10.1016/S0370-1573(02)00267-3 | url =http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVP-46SP0J5-1&_user=10&_coverDate=10/31/2002&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=1631f280c7f4234507b308c49b2598e3&searchtype=a|archiveurl = http://arxiv.org/abs/hep-th/0204253 | archivedate = 4 Jan 2008 }}</ref><ref>
{{cite journal | last1        = Grumiller | first1       = Daniel | authorlink1  = Daniel Grumiller | last2        = Meyer | first2       = Rene | authorlink2  = Rene Meyer | year         = 2006 | title        = Ramifications of Lineland | journal      = Turkish Journal of Physics| volume       = 30 | issue = 5 | pages        = 349&ndash;378 | url          = http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archiveurl   = http://arxiv.org/abs/hep-th/0604049 | archivedate  = 1 June 2006 }}
</ref> with the [[CGHS model]] or [[Liouville gravity]]. The action is given by
:<math>S = \frac{1}{\kappa}\int d^2x\, \sqrt{-g}\left[ -R\Phi - \frac{1}{2} g^{\mu \nu} \nabla_{\mu} \Phi \nabla_{\nu} \Phi - \Lambda + \kappa\mathcal{L}_{\text{mat}} \right]</math>
where &Phi; is the dilaton, <math> \nabla _{\mu} </math> denotes the [[covariant derivative]] and the equation of motion is
:<math>R-\Lambda=\kappa T</math>
The metric in this case is more amenable to analytical solutions than the general 3+1D case. For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the [[Lambert_W_function#Generalizations|Lambert W function]], even with an additional electromagnetic field (see [[Quantum_gravity#The_dilaton|quantum gravity]] and references for details).

== See also ==

* [[CGHS model]]
* [[Liouville gravity]]
* [[Quantum_gravity#The_dilaton|quantum gravity]]

== References ==

<references />

{{theories of gravitation}}
{{quantum gravity}}

{{DEFAULTSORT:Jackiw-Teitelboim gravity}}
[[Category:Theory of relativity]]


{{relativity-stub}}