Non-linear regime of the Generalized Minimal Massive Gravity in critical points

TL;DR

This paper explores the non-linear solutions of the Generalized Minimal Massive Gravity (GMMG) theory at critical points, revealing logarithmic behaviors in $AdS_3$ wave solutions and black hole deformations, with energy and angular momentum calculations.

Contribution

It provides exact non-linear solutions of GMMG at critical points, including $AdS_3$ waves and black hole deformations, and computes their conserved charges.

Findings

Logarithmic $AdS_3$ wave solutions at critical points

Logarithmic deformation of extremal BTZ black holes

Energy and angular momentum of solutions calculated using Abbott-Deser-Tekin method

Abstract

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 $AdS_3$ 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 $AdS_3$ wave solutions are present, and have logarithmic form in critical points. Then we study the $AdS_3$ 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.