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http://arxiv.org/abs/0904.1738
Symmetric space Cartan connections and gravity in three and four dimensions
Derek K. Wise
18 pages; Article prepared for special journal issue dedicated to Elie Cartan
(Submitted on 10 Apr 2009)
"Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant theories in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action. In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric structure of the model. I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1) and its relatives. Finally, I suggest that the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'."
http://arxiv.org/abs/0904.1595
Solutions to Horava Gravity
H. Lu, Jianwei Mei, C.N. Pope
8 pages
(Submitted on 10 Apr 2009)
"Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this paper, we derive the full set of equations of motion, and then we obtain spherically symmetric solutions and discuss their properties. We also obtain the Friedman-Lemaitre-Robertson-Walker cosmological metric."
http://arxiv.org/abs/0904.1657
Topological Interpretation of Barbero-Immirzi Parameter through a Rescaling of Wavefunctional
Sandipan Sengupta
(Submitted on 10 Apr 2009)
"The topological character of Barbero-Immirzi parameter ($\eta$) can emerge in a quantum description through a rescaling of the wavefunctional. This makes it possible to arrive at the canonical formulation for the action made up of the Hilbert-Palatini term and the Nieh-Yan invariant starting from the Hilbert-Palatini canonical theory. Here we set up a general rescaling procedure for gravity with or without matter. This needs a systematic treatment of the second class constraints (of Hilbert-Palatini theory) which are not solved before quantization. This allows a direct topological interpretation of eta in a quantum framework. This analysis can be carried out without choosing time gauge."
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