The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. In the present paper we obtain exact solutions to the GMMG field equations in the non-linear regime of the model. GMMG model about AdS3 space is conjectured to be dual to a 2- dimensional CFT. We study the theory in critical points corresponding to the central charges c− = 0 or c+ = 0, in the non-linear regime.We show that AdS3 wave solutions are present, and have logarithmic form in critical points. Then we study the AdS3 non-linear deformation solution. Furthermore we obtain logarithmic deformation of extremal BTZ black hole. After that using Abbott–Deser–Tekin method we calculate the energy and angular momentum of these types of black hole solutions.
