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

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

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