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

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

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. arXiv:1605.03431. doi:10.1103/PhysRevD.93.084017.