Modified BTZ black hole and some thermodynamical properties in dilaton/scalar gravity model

We construct a new class of black hole solutions of Einstein's gravity in the presence of dilaton/scalar fields. In this regard, we present a general action (Eq. () in the introduction) where Einstein's gravity is coupled with these fields. Using this action, we derive the equations of motion. Moreover, we employ n-dimensional static toroidal space-time as the background geometry. Our study reveals that the standard BTZ solution can be recovered from some of these solutions as a special case. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS ((anti-) de Sitter). We also show under which conditions these solutions behave (A)dS, asymptotically. Some basic thermodynamics of the black hole solution is also analyzed. The most important result derived from our study is that the presence of the dilaton field increases the tendency of temperature to be positive near the origin. Besides, when we investigate the black hole's stability, it is shown that the presence of this field makes the solutions to be more stable near the origin.