AdS Black Hole Solutions in the Extended New Massive Gravity

TL;DR

The study addresses AdS black hole solutions in three-dimensional extended NMG with two higher-curvature generalizations, the $R^3$-NMG and BI-NMG. Using a dimensional reduction approach and Wald entropy, the authors extract dual CFT central charges via Cardy formula $S_{BH} = \frac{\pi^2 L}{3}(c_L T_L + c_R T_R)$ with parity symmetry $c_L=c_R=c$, and validate these against a central charge function formalism for asymptotically AdS spacetimes. They construct BTZ, warped AdS, and new type black holes, obtaining explicit expressions for $c$ in each case and showing consistency with known NMG limits; new type black holes arise only in $R^3$-NMG and admit a natural boundary-based central charge. The results illuminate how higher curvature corrections shape holographic data and suggest avenues for further study, including linearized spectrum analysis and potential string theory embeddings.

Abstract

We have obtained (warped) AdS black hole solutions in the three dimensional extended new massive gravity. We investigate some properties of black holes and obtain central charges of the two dimensional dual CFT. To obtain the central charges, we use the relation between entropy and temperature according to the AdS/CFT dictionary. For AdS black holes, one can also use the central charge function formalism which leads to the same results.