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

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

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.^[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).

See also

• CGHS model
• Liouville gravity
• Quantum gravity

References

1. 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. doi:10.1016/0550-3213(90)90265-F. Archived from the original on Dec 1989.
2. Grumiller, Daniel; Kummer, Wolfgang; Vassilevich, Dmitri (October 2002). "Dilaton Gravity in Two Dimensions". Physics Reports 369 (4): 327–430. doi:10.1016/S0370-1573(02)00267-3. Archived from the original on 4 Jan 2008.
3. Grumiller, Daniel; Meyer, Rene (2006). "Ramifications of Lineland". Turkish Journal of Physics 30 (5): 349–378. Archived from the original on 1 June 2006.
4. 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. doi:10.1103/PhysRevD.93.084017.