BTZ black-hole dressed in the gravitational Chern-Simons term

We study the effect of the gravitational Chern-Simons term (GCST) in the (2+1)-dimensional anti-de Sitter (AdS(2+1)) geometry. In the context of the gauge gravity, we obtain a black-hole solution and its boundary Wess-Zumino-Witten (WZW) theory. The Ba (n) over tilde ados-Teitelboim-Zanelli (BTZ) black-hole solution can still be retrieved but its gravitational mass and angular momentum are different from their inherent values, The deformation of these quantities due to the GCST can be summarized as a combination of boosting and rescaling. The boundary WZW theory is found to be chiral, i.e., composed of the right-moving part and the left-moving part with different Kac-Moody levels. We show explicitly that the identification Killing vector used in the Einstein gravity to mode the AdS(2+1) spacetime to make a BTZ black-hole is nothing but the Wilson loop operator accounting for the holonomy around a point source in the gauge gravity. Assuming pure AdS(2+1) spacetime to be a black-hole vacuum, we show that the statistical entropy from the boundary conformal field theory (CFT) system satisfies the area law.