Jackiw–Teitelboim gravity

The R = T model, 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 with the CGHS model or Liouville gravity. The action is given by
 * $$S = \frac{1}{\kappa}\int d^2x\, \sqrt{-g}\, \Phi \left( R - \Lambda \right)$$

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