Jackiw–Teitelboim gravity

The R = T model, 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 with the CGHS model or Liouville gravity. The action is given by

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

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

$R-\Lambda =\kappa T$

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. 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).

See also

• CGHS model
• Liouville gravity
• Quantum gravity