Jackiw–Teitelboim gravity explained

The R = T model,^[1] also known as Jackiw–Teitelboim gravity (named after 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^{[2] [3]} with the CGHS model or Liouville gravity. The action is given by

S = (1)/(\kappa) \int d ^{2x} \sqrt{ - g} \Phi \left( R - Λ \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.^[4] 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.

By varying with respect to Φ, we get

R =Λ on shell, which means the metric is either Anti-de Sitter space or De Sitter space depending upon the sign of Λ.

Notes and References

1. Mann . Robert . Robert B. Mann . Shiekh . A. . Tarasov . L. . 3 Sep 1990 . Classical and quantum properties of two-dimensional black holes . Nuclear Physics . 341 . 1 . B . 134 - 154 . 10.1016/0550-3213(90)90265-F . 1990NuPhB.341..134M .
2. Grumiller . Daniel . Daniel Grumiller . Kummer . Wolfgang . Vassilevich . Dmitri . Dmitri Vassilevich . October 2002 . Dilaton Gravity in Two Dimensions . Physics Reports . 369 . 4 . 327 - 430 . 10.1016/S0370-1573(02)00267-3 . hep-th/0204253 . 2002PhR...369..327G . 119497628 .
3. Grumiller . Daniel . Daniel Grumiller . Meyer . Rene . Rene Meyer . 2006 . Ramifications of Lineland . . 30 . 5 . 349 - 378 . https://web.archive.org/web/20110822060534/http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 . 22 August 2011 . dead . hep-th/0604049 . 2006TJPh...30..349G .
4. Scott. T.C.. Zhang. Xiangdong. Mann. Robert. Fee. G.J.. Canonical reduction for dilatonic gravity in 3 + 1 dimensions. Physical Review D. 93. 8. 084017. 2016. 10.1103/PhysRevD.93.084017. 1605.03431. 2016PhRvD..93h4017S.