Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-09-02
Int.J.Mod.Phys.A25:4911-4932,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
To appear in International Journal of Modern Physics A
Scientific paper
10.1142/S0217751X10050561
A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang-Mills formulation for gravity in a $2+1$ dimensional space-time. In the massless case we show that the theory contains three degrees of freedom and only one is a non-unitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert-Einstein-Fierz-Pauli unitary massive theory plus three massless modes, two of them represents non-unitary ones. Finally we confirm the existence of a family of unitary Yang-Mills-extended theories which are classically consistent with Einstein's solutions coming from non massive and topologically massive gravity. The unitarity of these YM-extended theories is shown in a perturbative regime. A possible way to perform a non-perturbative study is remarked.
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