Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-01-24
Phys.Lett.B687:375-381,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages; minor changes, additional references
Scientific paper
10.1016/j.physletb.2010.03.043
We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the classical Drinfel'd double of a "hybrid" deformation of sl(2,R) that depends on two parameters (\eta,z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter \eta is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in \eta and z; we also investigate the limits of vanishing \eta and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively.
Ballesteros Angel
Herranz Francisco J.
Meusburger Catherine
No associations
LandOfFree
Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-696553