Jackiw–Teitelboim gravity

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

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

where \( \Phi 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.[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.
References

Mann, Robert; Shiekh, A.; Tarasov, L. (3 Sep 1990). "Classical and quantum properties of two-dimensional black holes". Nuclear Physics. B. 341 (1): 134–154. Bibcode:1990NuPhB.341..134M. doi:10.1016/0550-3213(90)90265-F.
Grumiller, Daniel; Kummer, Wolfgang; Vassilevich, Dmitri (October 2002). "Dilaton Gravity in Two Dimensions". Physics Reports. 369 (4): 327–430.arXiv:hep-th/0204253. Bibcode:2002PhR...369..327G. doi:10.1016/S0370-1573(02)00267-3.
Grumiller, Daniel; Meyer, Rene (2006). "Ramifications of Lineland". Turkish Journal of Physics. 30 (5): 349–378.arXiv:hep-th/0604049. Bibcode:2006TJPh...30..349G. Archived from the original on 22 August 2011.

Scott, T.C.; Zhang, Xiangdong; Mann, Robert; Fee, G.J. (2016). "Canonical reduction for dilatonic gravity in 3 + 1 dimensions". Physical Review D. 93 (8): 084017.arXiv:1605.03431. Bibcode:2016PhRvD..93h4017S. doi:10.1103/PhysRevD.93.084017.

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