What happens for the BTZ black hole solution in dilaton f(R)-gravity?

Abstract

In this work, we obtain the black hole solutions in the dilaton [Formula: see text]-gravity (R is not considered as a constant here) and investigate their thermodynamics especially phase transition and critical behavior in the anti-de Sitter (AdS) extended phase-space. We obtain the exact Banados, Teitelboim and Zanelli (BTZ) counterpart solutions in dilaton [Formula: see text]-gravity which is the basis of our work. We also obtain the exact form of [Formula: see text] model for some solutions. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for these solutions and we compare them with the BTZ corresponding quantities. After that, we investigate the stability (local and global) for these obtained solutions. In the critical behavior analysis, we find that there is no evidence to show the existence of P–V criticality (like the ordinary BTZ case) in this modified gravity model except some unusual P–V behavior in the corresponding diagrams.

Higher-dimensional black hole solutions with scalar hair and dilaton field and toroidal horizons and interior solution

“…Here we introduce the action of charged black holes in the Einstein-Maxwell gravity which is coupled to a dilaton field. The general form of this action is studied in literature [61,62,63,64]:…”

Thermodynamic geometric analysis of BTZ black hole in f(R,ϕ) Gravity

“…We first briefly review conformally dressed black holes. The role of the theory consists of a Ritchie scalar, a negative cosmological constant, and a conformally coupled scalar field, namely [8,9].…”

“…The (2+1)-dimensional dilaton gravitational sum studies the modification of the dilaton/scalar to the BTZ black hole. Recently, a regular black hole solution with a real scalar field coupled to a Maxwell field was constructed by dual transformation, and a (2 + 1)-dimensional regular black hole with a nonlinear electrodynamic source was studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

A novel f(R)-form solution for coupled gravity

“…First, we can consider the following equation (modified Einstein's equation of gravity).R1 is the curvature scalar of formula (3), and similarly defines R1 µν and R1 µν . The proper time of spherical coordinates is [1][2][3][4][5][6](The metric in which is in exponential form)…”