$(2+1)$-Dimensional Black Holes in $f(R,ϕ)$ Gravity

Abstract

We consider a f (R) gravity theory in (2 + 1)-dimensions with a self-interacting scalar field non-minimally coupled to gravity. Without specifying the form of the f (R) function, solving the field equations we find that the Ricci scalar receives a non-linear correction term which breaks the conformal invariance and leads to a massless black hole solution. When the non-linear term decouples, we get a well known hairy black hole solution with the scalar field conformally coupled to gravity. We also find that the entropy of our black hole may be higher than the corresponding conformal black hole which indicates that our solution may be thermodynamically preferred.

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].…”

“…We can immediately integrate the Ricci scalar f R (r) to obtain the general form of f (R, φ) theory [9] f R…”

“…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].…”