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).

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. doi:10.1016/0550-3213(90)90265-F. Archived from the original on Dec 1989.
↑ 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.
↑ Grumiller, Daniel; Meyer, Rene (2006). "Ramifications of Lineland". Turkish Journal of Physics. 30 (5): 349–378. Archived from the original on 1 June 2006.
↑ 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.

Theories of gravitation

Standard

Newtonian gravity (NG)	Newton's law of universal gravitation History of gravitational theory

General relativity (GR)	Introduction History Mathematics Resources Tests Post-Newtonian formalism Linearized gravity ADM formalism Gibbons–Hawking–York boundary term

Alternatives to
general relativity

Paradigms	Classical theories of gravitation Quantum gravity Theory of everything

Classical	Einstein–Cartan Bimetric theories Gauge theory gravity Teleparallelism Composite gravity f(R) gravity Massive gravity Modified Newtonian dynamics (MOND) Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström Whitehead Geometrodynamics Induced gravity Tensor–vector–scalar Chameleon Pressuron

Quantisation	Euclidean quantum gravity Canonical quantum gravity Wheeler–DeWitt equation Loop quantum gravity Spin foam Causal dynamical triangulation Causal sets DGP model

Unification	Kaluza–Klein theory Dilaton Supergravity

Unification and quantisation	Noncommutative geometry Self-creation cosmology Semiclassical gravity Superfluid vacuum theory Logarithmic BEC vacuum String theory M-theory F-theory Heterotic string theory Type I string theory Type 0 string theory Bosonic string theory Type II string theory Little string theory Twistor theory Twistor string theory

Generalisations / Extensions of GR	Scale relativity Liouville gravity Lovelock theory (2+1)-dimensional topological gravity Gauss–Bonnet gravity Jackiw–Teitelboim gravity

Pre-Newtonian theories
and Toy models

Quantum gravity

Central concepts

Toy models

Quantum field theory
in curved spacetime

Black holes

Approaches

String theory	Bosonic string theory M-theory Supergravity Superstring theory

Canonical quantum gravity	Loop quantum gravity Wheeler–DeWitt equation

Euclidean quantum gravity	Hartle–Hawking state

Others	Causal dynamical triangulation Causal sets Noncommutative geometry Spin foam Group field theory Superfluid vacuum theory Twistor theory

Applications

Quantum cosmology

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Jackiw–Teitelboim gravity

See also

References