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.

vte

Theories of gravitation

Standard

Newtonian gravity (NG)

Newton's law of universal gravitation Gauss's law for gravity Poisson's equation for gravity History of gravitational theory

General relativity (GR)

Introduction History Mathematics Exact solutions 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 Infinite derivative gravity Massive gravity Modified Newtonian dynamics, MOND

AQUAL Tensor–vector–scalar Nonsymmetric gravitation Scalar–tensor theories

Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories

Nordström Whitehead Geometrodynamics Induced gravity Chameleon Pressuron Degenerate Higher-Order Scalar-Tensor theories

Quantum-mechanical

Unified-field-theoric

Kaluza–Klein theory

Dilaton Supergravity

Unified-field-theoric and

quantum-mechanical

Noncommutative geometry 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

Liouville gravity Lovelock theory (2+1)-dimensional topological gravity Gauss–Bonnet gravity Jackiw–Teitelboim gravity

Pre-Newtonian

theories and

toy models

Aristotelian physics CGHS model RST model Mechanical explanations

Fatio–Le Sage Entropic gravity Gravitational interaction of antimatter Physics in the medieval Islamic world Theory of impetus

Related topics

vte

Quantum gravity

Central concepts

AdS/CFT correspondence Ryu-Takayanagi Conjecture Causal patch Gravitational anomaly Graviton Holographic principle IR/UV mixing Planck scale Quantum foam Trans-Planckian problem Weinberg–Witten theorem Faddeev-Popov ghost

Toy models

2+1D topological gravity CGHS model Jackiw–Teitelboim gravity Liouville gravity RST model Topological quantum field theory

Quantum field theory in curved spacetime

Bunch–Davies vacuum Hawking radiation Semiclassical gravity Unruh effect

Black hole complementarity Black hole information paradox Black-hole thermodynamics Bousso's holographic bound ER=EPR Firewall (physics) Gravitational singularity

Approaches

String theory

Bosonic string theory M-theory Supergravity Superstring theory

Loop quantum gravity Wheeler–DeWitt equation

Euclidean quantum gravity

Others

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

Applications

Quantum cosmology

Eternal inflation Multiverse FRW/CFT duality

Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License