Extremal Black Holes and Holographic C-Theorem

Understand

We found Bogomol'nyi type of the first order differential equations in three dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled.

• Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes.
• We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations.
• All these solutions have the anti de-Sitter spaces as their asymptotic geometries and as the near horizon ones.