Jackiw–Teitelboim gravity

Jackiw–Teitelboim gravity, also known as the R = T model,{{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 = 134–154 | doi = 10.1016/0550-3213(90)90265-F | bibcode= 1990NuPhB.341..134M }} or simply JT gravity (after physicists Roman Jackiw and Claudio Teitelboim), is a theory of gravity with dilaton coupling in one spatial and one time dimension. It should not be confused{{cite journal | last1 = Grumiller | first1 = Daniel | authorlink1 = Daniel Grumiller | last2 = Kummer | first2 = Wolfgang | last3 = Vassilevich | first3 = Dmitri | authorlink3 = Dmitri Vassilevich | date = October 2002 | title = Dilaton Gravity in Two Dimensions | journal = Physics Reports | volume = 369 | issue = 4 | pages = 327–430 | doi = 10.1016/S0370-1573(02)00267-3 | arxiv = hep-th/0204253 | bibcode = 2002PhR...369..327G | s2cid = 119497628 }}{{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 = 349–378 | url = http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archiveurl = https://web.archive.org/web/20110822060534/http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archivedate = 22 August 2011 | url-status = dead | arxiv = hep-th/0604049 | bibcode = 2006TJPh...30..349G }} with the CGHS model or Liouville gravity. The action is given by

:$S\; =\; \backslash frac\{1\}\{\backslash kappa\}\backslash int\; d^2x\backslash ,\; \backslash sqrt\{-g\}\backslash ,\; \backslash Phi\; \backslash left(\; R\; -\; \backslash Lambda\; \backslash right)$

The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained.{{cite journal|last1=Scott|first1=T.C.|last2=Zhang|first2=Xiangdong|last3=Mann|first3=Robert|last4=Fee|first4=G.J.|title=Canonical reduction for dilatonic gravity in 3 + 1 dimensions|journal=Physical Review D|volume=93|issue=8|pages=084017|date=2016|doi=10.1103/PhysRevD.93.084017|arxiv=1605.03431|bibcode=2016PhRvD..93h4017S}} 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, even with an additional electromagnetic field.

Varying with respect to Φ yields $R=\backslash Lambda$ on shell, which means the metric is either Anti-de Sitter space or De Sitter space, depending upon the sign of Λ.