Jackiw–Teitelboim gravity

The R = T model,[1] also known as Jackiw–Teitelboim gravity, 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

${\displaystyle S={\frac {1}{\kappa }}\int d^{2}x\,{\sqrt {-g}}\left[-R\Phi -{\tfrac {1}{2}}g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi -\Lambda +\kappa {\mathcal {L}}_{\text{mat}}\right]}$

where ${\displaystyle \Phi }$ is the dilaton, ${\displaystyle \nabla _{\mu }}$ denotes the covariant derivative and the equation of motion is

${\displaystyle R-\Lambda =\kappa T}$

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 (see quantum gravity and references for details).