Black holes of $(2+1)$-dimensional $f(R)$ gravity coupled to a scalar field

Abstract

We consider f (R) gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential in (2 + 1)-dimensions. Without specifying the form of the f (R) function, we first obtain an exact black hole solution dressed with scalar hair with the scalar charge to appear in the f (R) function and we discuss its thermodynamics. This solution at large distances gives a hairy BTZ black hole, and it reduces to the BTZ black hole when the scalar field decouples. In a pure f (R) gravity supported by the scalar field, we find an exact hairy black hole similar to the BTZ black hole with phantom hair and an analytic f (R) form and discuss its thermodynamics. CONTENTS I. Introduction 1 II. The setup-derivation of the field equations 2 A. Without self-interacting potential 3 B. With self-interacting potential 3 III. Black hole solutions 4 A. c 1 = 1, c 2 = 0 4 B. Exact Black Hole Solution with Phantom Hair 9 IV. Conclusions 12 Acknowledgments 12 References 12

Exact Black Hole Solutions with a Conformally Coupled Scalar Field and Dynamic Ricci Curvature in $f(R)$ Gravity Theories

“…In [36], dynamical black holes, characterized by time-varying apparent horizons, in various theories of gravity, including the f (R) theory were investigated. The possibility of scalarization of black holes in the context of f (R) gravity was discussed in [37] and (2 + 1)-dimensional black holes with a minimally coupled self-interacting scalar field in the context of f (R) gravity was discussed in [41]. Recently non-trivial black hole solutions were investigated [42][43][44].…”

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

“…where C is an integration constant with the unit [L] −2 , related to the cosmological constant. This expression shows that a geometric correction term appears in addition to the Einstein-Hilbert term, while the scalar field does not appear immediately in the f (R) model as happens in [65].…”

“…Static and spherically symmetric black hole solutions were investigated with constant curvature, with and without electric charge and cosmological constant in [59][60][61]. Scalar fields have been recently introduced as matter fields in the context of f (R), exact black hole solutions have been found and the corresponding physical properties have been investigated in [63][64][65], while the stability of f (R) black holes was also considered in [66]. The possibility of dressing the black hole with a gravitational hair has also been discussed in [67,68].…”

New black hole solutions in three-dimensional $\mathit{f(R)}$ gravity

“…Thus, it is important to check Eqs. (3) and (5) to a spherically symmetric ansatz having two unknown functions [89].…”